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## 2

2
Simulation Examples

This chapter presents several examples of simulations that can be performed
by devising a simulation table either manually or with a spreadsheet. The
simulation table provides a systematic method for tracking system state over
time. These examples provide insight into the methodology of discrete system
simulation and the descriptive statistics used for predicting system performance.

The simulations in this chapter entail three steps:

1. Determine the characteristics of each of the inputs to the simulation.
Quite often, these may be modeled as probability distributions, either
continuous or discrete.

2. Construct a simulation table. Each simulation table is different, for each
is developed for the problem at hand. An example of a simulation ta-
ble is shown in Table 2.1. In this example there are p inputs, xij , j =
1, 2, . . . , p, and one response, yi , for each of repetitions i = 1, 2, . . . , n.
Initialize the table by filling in the data for repetition 1.

3. For each repetition i , generate a value for each of the p inputs, and eval-
uate the function, calculating a value of the response yi . The input values
may be computed by sampling values from the distributions determined
in step 1. A response typically depends on the inputs and one or more
previous responses.

This chapter gives a number of simulation examples in queueing, inven-
tory, and reliability. The two queueing examples provide a single-server and

23

24 Chap. 2 Simulation Examples

two-server system, respectively. (Chapter 6 provides more insight into queue-
ing models.) The first inventory example involves a problem that has a closed-
form solution; thus the simulation solution can be compared to the mathemat-
ical solution. The second inventory example pertains to the classic order-level
model.

Finally, there is an example that introduces the concept of random normal
numbers and a model for the determinination of lead-time demand.

2.1 Simulation of Queueing Systems

A queueing system is described by its calling population, the nature of the ar-
rivals, the service mechanism, the system capacity, and the queueing discipline.
These attributes of a queueing system are described in detail in Chapter 6. A
simple single-channel queueing system is portrayed in Figure 2.1.

Server
Waiting line

Calling population

Figure 2.1 Queueing system.

In the single-channel queue, the calling population is infinite; that is, if a
unit leaves the calling population and joins the waiting line or enters service,
there is no change in the arrival rate of other units that may need service.
Arrivals for service occur one at a time in a random fashion; once they join the
waiting line, they are eventually served. In addition, service times are of some
random length according to a probability distribution which does not change
over time. The system capacity has no limit, meaning that any number of units
can wait in line. Finally, units are served in the order of their arrival (often
called FIFO: first in, first out) by a single server or channel.

Table 2.1 Simulation Table
Inputs

Response

Repetitions xi1 xi2 · · · xij · · · xip yi
1

2

3

·
·
·
n

Sec. 2.1 Simulation of Queueing Systems 25

Arrivals and services are defined by the distribution of the time between
arrivals and the distribution of service times, respectively. For any simple single-
or multi-channel queue, the overall effective arrival rate must be less than the
total service rate, or the waiting line will grow without bound. When queues
grow without bound, they are termed “explosive” or unstable. (In some reen-
trant queueing networks in which units return a number of times to the same
server before finally exiting the system, the condition about arrival rate being
less than service rate may not guarantee stability. See Harrison and Nguyen
[1995] for more explanation. Interestingly, this type of instability was noticed
first, not in theory, but in actual manufacturing in semiconductor plants.) More
complex situations may occur—for example, arrival rates that are greater than
service rates for short periods of time, or networks of queues with routing.
However, this chapter sticks to the simplest, more basic queues.

Prior to introducing several simulations of queueing systems, it is neces-
sary to understand the concepts of system state, events, and simulation clock.
(These concepts are studied systematically in Chapter 3.) The state of the sys-
tem is the number of units in the system and the status of the server, busy or
idle. An event is a set of circumstances that cause an instantaneous change in
the state of the system. In a single-channel queueing system there are only two
possible events that can affect the state of the system. They are the entry of a
unit into the system (the arrival event) or the completion of service on a unit
(the departure event). The queueing system includes the server, the unit being
serviced (if one is being serviced), and units in the queue (if any are waiting).
The simulation clock is used to track simulated time.

If a unit has just completed service, the simulation proceeds in the manner
shown in the flow diagram of Figure 2.2. Note that the server has only two
possible states: it is either busy or idle.

Departure
event

No Yes Remove the waiting unit
from the queue

Begin servicing
the unit

Begin server
idle time

Another
unit waiting

?

Figure 2.2 Service-just-completed flow diagram.

The arrival event occurs when a unit enters the system. The flow diagram
for the arrival event is shown in Figure 2.3. The unit may find the server either
idle or busy; therefore, either the unit begins service immediately, or it enters the
queue for the server. The unit follows the course of action shown in Figure 2.4.

26 Chap. 2 Simulation Examples

Arrival
event

Unit enters
service

Unit enters
queue for
service

No YesServer
busy

?

Figure 2.3 Unit-entering-system flow diagram.

If the server is busy, the unit enters the queue. If the server is idle and the
queue is empty, the unit begins service. It is not possible for the server to be
idle and the queue to be nonempty.

Not empty

Enter queue

Impossible

Empty

Enter queue

Enter service

Busy

Idle

Server
status

Queue status

Figure 2.4 Potential unit actions upon
arrival.

After the completion of a service the server may become idle or remain
busy with the next unit. The relationship of these two outcomes to the status
of the queue is shown in Figure 2.5. If the queue is not empty, another unit
will enter the server and it will be busy. If the queue is empty, the server will
be idle after a service is completed. These two possibilities are shown as the
shaded portions of Figure 2.5. It is impossible for the server to become busy if
the queue is empty when a service is completed. Similarly, it is impossible for
the server to be idle after a service is completed when the queue is not empty.

Not empty

Impossible

Empty

ImpossibleBusy

Idle

Server
outcomes

Queue status

Figure 2.5 Server outcomes after service
completion.

Now, how can the events described above occur in simulated time? Sim-
ulations of queueing systems generally require the maintenance of an event
list for determining what happens next. The event list tracks the future times

Sec. 2.1 Simulation of Queueing Systems 27

at which the different types of events occur. Simulations using event lists are
described in Chapter 3. This chapter simplifies the simulation by tracking each
unit explicitly. Simulation clock times for arrivals and departures are computed
in a simulation table customized for each problem. In simulation, events usu-
ally occur at random times, the randomness imitating uncertainty in real life.
For example, it is not known with certainty when the next customer will arrive
at a grocery checkout counter, or how long the bank teller will take to complete
a transaction. In these cases, a statistical model of the data is developed from
either data collected and analyzed, or subjective estimates and assumptions.

The randomness needed to imitate real life is made possible through the
use of “random numbers.” Random numbers are distributed uniformly and
independently on the interval (0, 1). Random digits are uniformly distributed
on the set {0, 1, 2, . . . , 9}. Random digits can be used to form random numbers
by selecting the proper number of digits for each random number and placing
a decimal point to the left of the value selected. The proper number of digits
is dictated by the accuracy of the data being used for input purposes. If the
input distribution has values with two decimal places, two digits are taken from
a random-digits table (such as Table A.1) and the decimal point is placed to the
left to form a random number.

Random numbers can also be generated in simulation packages and in
spreadsheets such as Excel® . For example, Excel has a macro function called
RAND() that returns a “random” number between 0 and 1. When numbers
are generated using a procedure, they are often referred to as pseudo-random
numbers. Since the method is known, it is always possible to know the sequence
of numbers that will be generated prior to the simulation. The most commonly
used methods for generating random numbers are discussed in Chapter 7.

In a single-channel queueing system interarrival times and service times
are generated from the distributions of these random variables. The examples
that follow show how such times are generated. For simplicity, assume that the
times between arrivals were generated by rolling a die five times and recording
the up face. Table 2.2 contains a set of five interarrival times generated in this
manner. These five interarrival times are used to compute the arrival times of
six customers at the queueing system.

Table 2.2 Interarrival and Clock
Times

Interarrival Arrival

Customer Time Time on Clock

1 − 0
2 2 2

3 4 6

4 1 7

5 2 9

6 6 15

28 Chap. 2 Simulation Examples

Table 2.3 Service
Times

Service

Customer Time

1 2

2 1

3 3

4 2

5 1

6 4

The first customer is assumed to arrive at clock time 0. This starts the
clock in operation. The second customer arrives two time units later, at a clock
time of 2. The third customer arrives four time units later, at a clock time of 6;
and so on.

The second time of interest is the service time. Table 2.3 contains service
times generated at random from a distribution of service times. The only possi-
ble service times are one, two, three, and four time units. Assuming that all four
values are equally likely to occur, these values could have been generated by
placing the numbers one through four on chips and drawing the chips from a hat
with replacement, being sure to record the numbers selected. Now, the inter-
arrival times and service times must be meshed to simulate the single-channel
queueing system. As shown in Table 2.4, the first customer arrives at clock
time 0 and immediately begins service, which requires two minutes. Service is
completed at clock time 2. The second customer arrives at clock time 2 and is
finished at clock time 3. Note that the fourth customer arrived at clock time 7,
but service could not begin until clock time 9. This occurred because customer
3 did not finish service until clock time 9.

Table 2.4 was designed specifically for a single-channel queue which serves
customers on a first-in, first-out (FIFO) basis. It keeps track of the clock time

Table 2.4 Simulation Table Emphasizing Clock Times
A B C D E

Arrival Time Service Service Time Service

Customer Time Begins Time Ends

Number (Clock) (Clock) (Duration) (Clock)

1 0 0 2 2

2 2 2 1 3

3 6 6 3 9

4 7 9 2 11

5 9 11 1 12

6 15 15 4 19

Sec. 2.1 Simulation of Queueing Systems 29

Table 2.5 Chronological
Ordering of
Events

Customer Clock

Event Type Number Time

Arrival 1 0

Departure 1 2

Arrival 2 2

Departure 2 3

Arrival 3 6

Arrival 4 7

Departure 3 9

Arrival 5 9

Departure 4 11

Departure 5 12

Arrival 6 15

Departure 6 19

at which each event occurs. The second column of Table 2.4 records the clock
time of each arrival event, while the last column records the clock time of each
departure event. The occurrence of the two types of events in chronological
order is shown in Table 2.5 and Figure 2.6.

4
0

1

2

N
u

m
b

e
r

o
f
cu

st
o

m
e

rs
in

t
h

e
s

ys
tt
e

m

8 12 16 20

Clock time

1 2 3 4 5

4 5

6

Figure 2.6 Number of customers in the system.

It should be noted that Table 2.5 is ordered by clock time, in which case
the events may or may not be ordered by customer number. The chronological
ordering of events is the basis of the approach to discrete-event simulation
described in Chapter 3.

Figure 2.6 depicts the number of customers in the system at the various
clock times. It is a visual image of the event listing of Table 2.5. Customer 1

30 Chap. 2 Simulation Examples

Table 2.6 Distribution of Time Between Arrivals
Time between

Arrivals Cumulative Random-Digit

(Minutes) Probability Probability Assignment

1 0.125 0.125 001−125
2 0.125 0.250 126−250
3 0.125 0.375 251−375
4 0.125 0.500 376−500
5 0.125 0.625 501−625
6 0.125 0.750 626−750
7 0.125 0.875 751−875
8 0.125 1.000 876−000

is in the system from clock time 0 to clock time 2. Customer 2 arrives at clock
time 2 and departs at clock time 3. No customers are in the system from clock
time 3 to clock time 6. During some time periods two customers are in the
system, such as at clock time 8, when both customers 3 and 4 are in the system.
Also, there are times when events occur simultaneously, such as at clock time
9, when customer 5 arrives and customer 3 departs.

Example 2.1 follows the logic described above while keeping track of
a number of attributes of the system. Example 2.2 is concerned with a two-
channel queueing system. The flow diagrams for a multichannel queueing
system are slightly different from those for a single-channel system. The devel-
opment and interpretation of these flow diagrams is left as an exercise for the

EXAMPLE 2.1 Single-Channel Queue
A small grocery store has only one checkout counter. Customers arrive at this
checkout counter at random from 1 to 8 minutes apart. Each possible value of
interarrival time has the same probability of occurrence, as shown in Table 2.6.
The service times vary from 1 to 6 minutes with the probabilities shown in
Table 2.7. The problem is to analyze the system by simulating the arrival and
service of 20 customers.

Table 2.7 Service-Time Distribution
Service Time Cumulative Random-Digit

(Minutes) Probability Probability Assignment

1 0.10 0.10 01−10
2 0.20 0.30 11−30
3 0.30 0.60 31−60
4 0.25 0.85 61−85
5 0.10 0.95 86−95
6 0.05 1.00 96−00

Sec. 2.1 Simulation of Queueing Systems 31

In actuality, 20 customers is too small a sample size to allow drawing any
reliable conclusions. The accuracy of the results is enhanced by increasing the
sample size, as discussed in Chapter 11. However, the purpose of the exercise
is to demonstrate how simple simulations can be carried out in a table, either
manually or with a spreadsheet, not to recommend changes in the grocery store.
A second issue, discussed thoroughly in Chapter 11, is that of initial conditions.
A simulation of a grocery store that starts with an empty system is not realistic
unless the intention is to model the system from startup or to model until steady-
state operation is reached. Here, to keep things simple, starting conditions and
concerns are overlooked.

A set of uniformly distributed random numbers is needed to generate
the arrivals at the checkout counter. Random numbers have the following
properties:

1. The set of random numbers is uniformly distributed between 0 and 1.
2. Successive random numbers are independent.

With tabular simulations, random digits such as those found in Table A.1 in
the Appendix can be converted to random numbers. If using a spreadsheet,
most have a built-in random-number generator such as RAND() in Excel. The
example in the text uses random digits from Table A.1; in some of the exercises

Random digits are converted to random numbers by placing a decimal
point appropriately. Since the probabilities in Table 2.6 are accurate to 3 signif-
icant digits, three-place random numbers will suffice. It is necessary to list only
19 random numbers to generate times between arrivals. Why only 19 numbers?
The first arrival is assumed to occur at time 0, so only 19 more arrivals need to
be generated to end up with 20 customers. Similarly, for Table 2.7, two-place
random numbers will suffice.

The rightmost two columns of Tables 2.6 and 2.7 are used to generate ran-
dom arrivals and random service times. The third column in each table contains
the cumulative probability for the distribution. The rightmost column contains
the random digit-assignment. In Table 2.6, the first random-digit assignment
is 001–125. There are 1000 three-digit values possible (001 through 000). The
probability of a time-between-arrivals of 1 minute is 0.125, and 125 of the 1000
random-digit values are assigned to such an occurrence. Times between ar-
rivals for 19 customers are generated by listing 19 three-digit values from Table
A.1 and comparing them to the random-digit assignment of Table 2.6.

For manual simulations, it is good practice to start at a random position in
the random-digit table and proceed in a systematic direction, never re-using the
same stream of digits in a given problem. If the same pattern is used repeatedly,
bias could result, because the same event pattern would be generated. In Excel,
each time the random function RAND() is evaluated, it returns a new random
value.

The time-between-arrival determination is shown in Table 2.8. Note that
the first random digits are 913. To obtain the corresponding time between

32 Chap. 2 Simulation Examples

Table 2.8 Time-Between-Arrivals Determination
Time between Time between

Random Arrivals Random Arrivals

Customer Digits (Minutes) Customer Digits (Minutes)

1 − − 11 109 1
2 913 8 12 093 1

3 727 6 13 607 5

4 015 1 14 738 6

5 948 8 15 359 3

6 309 3 16 888 8

7 922 8 17 106 1

8 753 7 18 212 2

9 235 2 19 493 4

10 302 3 20 535 5

arrivals, enter the fourth column of Table 2.6 and read 8 minutes from the first
column of the table. Alternatively, we see that 0.913 is between the cumulative
probabilities 0.876 and 1.000, again resulting in 8 minutes as the generated time.

Service times for all 20 customers are shown in Table 2.9. These service
times were generated based on the methodology described above, together with
the aid of Table 2.7. The first customer’s service time is 4 minutes because the
random digits 84 fall in the bracket 61– 85, or alternatively because the derived
random number 0.84 falls between the cumulative probabilities 0.61 and 0.85.

Table 2.9 Service Times Generated
Service Service

Random Time Random Time

Customer Digits (Minutes) Customer Digits (Minutes)

1 84 4 11 32 3

2 10 1 12 94 5

3 74 4 13 79 4

4 53 3 14 05 1

5 17 2 15 79 5

6 79 4 16 84 4

7 91 5 17 52 3

8 67 4 18 55 3

9 89 5 19 30 2

10 38 3 20 50 3

Sec. 2.1 Simulation of Queueing Systems 33

The essence of a manual simulation is the simulation table. These ta-
bles are designed for the problem at hand, with columns added to answer the
questions posed. The simulation table for the single-channel queue, shown in
Table 2.10, is an extension of the type of table already seen in Table 2.4. The
first step is to initialize the table by filling in cells for the first customer. The
first customer is assumed to arrive at time 0. Service begins immediately and
finishes at time 4. The customer was in the system for 4 minutes. After the
first customer, subsequent rows in the table are based on the random numbers
for interarrival time and service time and the completion time of the previous
customer. For example, the second customer arrives at time 8. Thus, the server
(checkout person) was idle for 4 minutes. Skipping down to the fourth cus-
tomer, it is seen that this customer arrived at time 15 but could not be served
until time 18. This customer had to wait in the queue for 3 minutes. This pro-
cess continues for all 20 customers. Extra columns have been added to collect
statistical measures of performance such as each customer’s time in the system
and the server’s idle time (if any) since the previous customer departed. In
order to compute summary statistics, totals are formed as shown for service
times, time customers spend in the system, idle time of the server, and time the
customers wait in the queue.

In the exercises, the reader is asked to implement the simulation table for
the single-channel queue, Table 2.10, in Excel or another spreadsheet. Here
we give some hints when using Excel. The key column to compute is column
E, the “Time Service Begins”. (We leave for the reader the question of how to
compute the random interarrival and service times, but suggest the RAND()
random number generator or other built-in distribution in Excel.) First, the
reader may fill in row 1 for the first customer manually. The values for the
remaining customers must use macro formulas (which begin with an equals
sign in Excel). Note that a customer begins service at the later of its own
arrival time (column C) or the completion time (column G) of the previous
customer. Therefore, for customer 10, service begins at E10 = MAX(C10,
G9), where MAX() is the Excel macro function that returns the maximum
value in a range or list of cells. This easily generalizes to other customers.
(The statistical measures in columns H and I are easily computed by simple
sheet model: instead of using a random function for arrivals and service times,
type in the actual values given in Table 2.10 in columns B and D. If your for-
mulas are correct, the spreadsheet should duplicate Table 2.10 exactly. After
verification, replace the numbers by an appropriate random function. Then
on each recalculation of the spreadsheet (function key F9 in Excel), it will
generate new random numbers and you will get a new ‘’run” of the simula-
tion.

Some of the findings from the simulation in Table 2.10 are as follows:

34 Chap. 2 Simulation Examples

1. The average waiting time for a customer is 2.8 minutes. This is determined
in the following manner:

average waiting time
(minutes)

= total time customers wait in queue (minutes)
total numbers of customers

= 56
20

= 2.8 minutes
2. The probability that a customer has to wait in the queue is 0.65. This is

determined in the following manner:

probability (wait) = number of customers who wait
total number of customers

= 13
20

= 0.65
3. The fraction of idle time of the server is 0.21. This is determined in the

following manner:

probability of idle
server

= total idle time of server (minutes)
total run time of simulation (minutes)

= 18
86

= 0.21
The probability of the server being busy is the complement of 0.21, or
0.79.

4. The average service time is 3.4 minutes, determined as follows:

average service time
(minutes)

= total service time (minutes)
total number of customers

= 68
20

= 3.4 minutes
This result can be compared with the expected service time by finding the
mean of the service-time distribution using the equation

E(S) =
∞∑

s=0
sp(s)

Applying the expected-value equation to the distribution in Table 2.7
gives an expected service time of:

= 1(0.10) + 2(0.20) + 3(0.30) + 4(0.25) + 5(0.10) + 6(0.05)
= 3.2 minutes

The expected service time is slightly lower than the average service time
in the simulation. The longer the simulation, the closer the average will
be to E(S).

Se
c.

2
.1

Sim
u

la
tio

n
o

f
Q

u
e

u
e

in
g

Syste
m

s
3

5

Table 2.10 Simulation Table for Queueing Problem

A B C D E F G H I
Time Since Service Time Time Customer Time Time Customer Idle Time
Last Arrival Arrival Time Service Waits in Queue Service Spends in System of Server

Customer (Minutes) Time (Minutes) Begins (Minutes) Ends (Minutes) (Minutes)
1 − 0 4 0 0 4 4 0
2 8 8 1 8 0 9 1 4
3 6 14 4 14 0 18 4 5
4 1 15 3 18 3 21 6 0
5 8 23 2 23 0 25 2 2
6 3 26 4 26 0 30 4 1
7 8 34 5 34 0 39 5 4
8 7 41 4 41 0 45 4 2
9 2 43 5 45 2 50 7 0

10 3 46 3 50 4 53 7 0
11 1 47 3 53 6 56 9 0
12 1 48 5 56 8 61 13 0
13 5 53 4 61 8 65 12 0
14 6 59 1 65 6 66 7 0
15 3 62 5 66 4 71 9 0
16 8 70 4 71 1 75 5 0
17 1 71 3 75 4 78 7 0
18 2 73 3 78 5 81 8 0
19 4 77 2 81 4 83 6 0
20 5 82 3 83 1 86 4 0

68 56 124 18

36 Chap. 2 Simulation Examples

5. The average time between arrivals is 4.3 minutes. This is determined in
the following manner:

average time between
arrivals (minutes)

=
sum of all times

between arrivals (minutes)
number of arrivals −1

= 82
19

= 4.3 minutes

One is subtracted from the denominator because the first arrival is as-
sumed to occur at time 0. This result can be compared to the expected
time between arrivals by finding the mean of the discrete uniform dis-
tribution whose endpoints are a = 1 and b = 8. The mean is given
by

E(A) = a + b
2

= 1 + 8
2

= 4.5 minutes

The expected time between arrivals is slightly higher than the average.
However, as the simulation becomes longer, the average value of the time
between arrivals will approach the theoretical mean, E(A).

6. The average waiting time of those who wait is 4.3 minutes. This is deter-
mined in the following manner:

Average waiting time of
those who wait (minutes)

= total time customers wait in queue (minutes)
total number of customers who wait

= 56
13

= 4.3 minutes

7. The average time a customer spends in the system is 6.2 minutes. This
can be determined in two ways. First, the computation can be achieved
by the following relationship:

average time customer

spends in the system

(minutes)

=
total time customers spend in the

system (minutes)
total number of customers

= 124
20

= 6.2 minutes

The second way of computing this same result is to realize that the fol-
lowing relationship must hold:

average time average time average time
customer spends customer spends customer spends

in the system = waiting in the + in service
(minutes) queue (minutes) (minutes)

Sec. 2.1 Simulation of Queueing Systems 37

From findings 1 and 4 this results in:

Average time customer spends in the system (minutes)

= 2.8 + 3.4 = 6.2 minutes
A decision maker would be interested in results of this type, but a longer

simulation would increase the accuracy of the findings. However, some sub-
jective inferences can be drawn at this point. Most customers have to wait;
however, the average waiting time is not excessive. The server does not have
an undue amount of idle time. Objective statements about the results would
depend on balancing the cost of waiting with the cost of additional servers.
(Simulations requiring variations of the arrival and service distributions, as
well as implementation in a spreadsheet, are presented as exercises for the

EXAMPLE 2.2 The Able Baker Carhop Problem
This example illustrates the simulation procedure when there is more than one
service channel. Consider a drive-in restaurant where carhops take orders and
bring food to the car. Cars arrive in the manner shown in Table 2.11. There are
two carhops—Able and Baker. Able is better able to do the job and works a bit
faster than Baker. The distribution of their service times is shown in Tables 2.12
and 2.13.

Table 2.11 Interarrival Distribution of Cars
Time between

Arrivals Cumulative Random-Digit

(Minutes) Probability Probability Assignment

1 0.25 0.25 01−25
2 0.40 0.65 26−65
3 0.20 0.85 66−85
4 0.15 1.00 86−00

The simulation proceeds in a manner similar to Example 2.1, except that
it is more complex because of the two servers. A simplifying rule is that Able
gets the customer if both carhops are idle. Perhaps, Able has seniority. (The

Table 2.12 Service Distribution of Able
Service Time Cumulative Random-Digit

(Minutes) Probability Probability Assignment

2 0.30 0.30 01−30
3 0.28 0.58 31−58
4 0.25 0.83 59−83
5 0.17 1.00 84−00

38 Chap. 2 Simulation Examples

Table 2.13 Service Distribution of Baker
Service Time Cumulative Random-Digit

(Minutes) Probability Probability Assignment

3 0.35 0.35 01−35
4 0.25 0.60 36−60
5 0.20 0.80 61−80
6 0.20 1.00 81−00

solution would be different if the decision were made at random or by any other
rule.)

The problem is to find how well the current arrangement is working.
To estimate the system measures of performance, a simulation of 1 hour of
operation is made. A longer simulation would yield more reliable results, but
for purposes of illustration a l-hour period has been selected.

The simulation proceeds in a manner similar to Example 2.1. Here there
are more events: a customer arrives, a customer begins service from Able, a
customer completes service from Able, a customer begins service from Baker,
and a customer completes service from Baker. The simulation table is shown
in Table 2.14.

In later exercises, the reader is asked to implement the simulation table,
Table 2.14, in a spreadsheet such as Excel. Here we provide a few hints (and
rules!). The row for the first customer is filled in manually, with the random-
number function RAND() or another random function replacing the random
digits. After the first customer, the cells for the other customers must be based
on logic and formulas. For example, the “Clock Time of Arrival” (column D)
in the row for the second customer is computed as follows:

D2 = D1 + C2

using notation similar to that used by most spreadsheets. (C2 is the time be-
tween arrivals 1 and 2.) This formula is easily generalized for any customer.

The logic to compute who gets a given customer, and when that service
begins, is more complex. Here we give a hint using the Excel macro function
IF(), which returns one of two values depending on whether a condition is true
or false. [The syntax is IF( condition, value if true, value if false).] The logic
goes as follows when a customer arrives: If the customer finds Able idle, the
customer begins service immediately with Able. If Able is not idle but Baker is,
then the customer begins service immediately with Baker. If both are busy, the

Sec. 2.1 Simulation

## 2

Running Head: PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT

IE 300: Industrial Engineering Seminar

Fall 2018

Deliverable 3

Title: Public Hospital Analysis of Bed Capacity in Kuwait

Group F12

Due Date: 29-Nov-18

Student Name ID’s

Anaam Jumaah 25520

Fatemah AlMuwail 23071

Hour AlJumah 25496

Mariam AlQassar 23924

Sarah AlMutairi 25523

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 2

Abstract …………………………………………………………………………………………………………………………. 5

Introduction ……………………………………………………………………………………………………………………. 6

Literature review …………………………………………………………………………………………………………….. 7

Health care system and resources ………………………………………………………………………………….. 8

Health care cost: ………………………………………………………………………………………………………… 11

Analysis of bed capacity …………………………………………………………………………………………….. 17

Benefit of bed capacity …………………………………………………………………………………………… 17

Occupancy rate………………………………………………………………………………………………………. 18

Utilization …………………………………………………………………………………………………………….. 18

Simulation …………………………………………………………………………………………………………….. 19

SWOT Analysis ………………………………………………………………………………………………………… 22

Strengths ………………………………………………………………………………………………………………. 23

Weaknesses …………………………………………………………………………………………………………… 24

Opportunities…………………………………………………………………………………………………………. 24

Threats………………………………………………………………………………………………………………….. 25

Background ………………………………………………………………………………………………………………….. 25

Problem Definition………………………………………………………………………………………………………… 30

Objectives ……………………………………………………………………………………………………………………. 30

Methodology ………………………………………………………………………………………………………………… 30

The scope of the problem ……………………………………………………………………………………………. 30

Define the problem ……………………………………………………………………………………………………. 31

Objectives ………………………………………………………………………………………………………………… 31

Literature Review………………………………………………………………………………………………………. 32

Data collection ………………………………………………………………………………………………………….. 32

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 3

Analysis……………………………………………………………………………………………………………………. 32

PDSA Cycle ……………………………………………………………………………………………………………… 35

Conclusion …………………………………………………………………………………………………………………… 37

References ……………………………………………………………………………………………………………………. 38

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 4

List of Tables and Figures

Figure 1 Data of MTH …………………………………………………………………………………………………… 13

Figure 2 Unit cost of inpatient units’ schedule ………………………………………………………………….. 14

Figure 3 Unit cost of outpatient schedule …………………………………………………………………………. 14

Figure 4 The cost variation of hospital components …………………………………………………………… 15

Figure 5 Health spending ……………………………………………………………………………………………….. 16

Figure 6 Simulated bed usage at various percentiles by day ……………………………………………….. 21

Figure 7 Estimated monthly bed requirements for peak demand at the 50th percentile…………… 22

Figure 8 Number of beds in public hospitals …………………………………………………………………….. 28

Figure 9 Bed capacity in each quarter in each hospital ………………………………………………………. 29

Figure 10 Flow Chart of the Methodology ……………………………… Error! Bookmark not defined.

Table 1: Old and new improvement of bed capacity of public health care in Kuwait …………….. 27

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 5

Abstract

The main objective of this project is to analyze the sufficiency of bed capacity in public

hospitals in Kuwait. The main purpose of the project is to study health care in Kuwait with a focus

on bed capacity; the problem and the background of this problem. After the study and research,

the project objective and the result of this investigation will be concluded.

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 6

Introduction

Healthcare system is a set of administrations that cares about diagnoses prevention and

provide the community patients the proper care. All governments in all countries care about health,

health administration is essential because it maintain rights of human beings. For example, Kuwait

ministry of health is working hard to provide comprehensive health care for citizens and resident

to protect them from damage of physical, psychological and social side. Moreover, try to provide

all kinds of health services like remedial and emergencies causes.

Kuwaiti health system is divided into 3 levels, these levels include hospitals, specialized

clinics and dispensaries. The first level is Primary care which is group of local clinics which are

the dispensaries located in each area. The second level is Secondary care includes six public

hospitals which are AlSabah Hospital, AlAmiri Hospital, AlAdan Hospital, AlFarwaniya Hospital,

Mubarak Al-Kabeer Hospital and AlJahra Hospital and the third level is Tertiary care includes 12

specialized clinics which are AlRazi, Physical Med.&Rehab, Maternity, Chest Disease, Infection

Disease, Psychological Medicine, Ibn Sina, Kuwait Cancer Control Center, Allergy Center,

Palliative Care, Sabah AlAhmad Urology Center and Zain. Also, the system includes 11 private

hospitals which are Dar Al Shifa Hospital, London Hospital, New Mowasat Hospital, Al Salam

International Hospital, Al Hadi Hospital, Royale Hayat Hospital, Sidra Hospital, Aliya

International Hospital, Al Seef Hospital, Al Rashid Hospital and Taiba Hospital.

Healthcare resources are essential to perform and deliver health services. The resources are

doctors, nurses, beds, and pharmacies. In addition, the number of doctors and nurses in each

hospital department is related to the number of beds in the department. So, if the number of beds

in the department are increased, the number of doctors and nurses in the hospital will have to be

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 7

increased too. Also, number of beds are required to be divided according to the need of the

hospitals and departments.

Bed capacity of health care is the number of beds which the hospital has. It’s important to

know if the number of beds are enough or not for the community. Bed occupancy and the ratio of

beds per population help in bed capacity managing. The prior objective according to the analysis

that will be done is about bed capacity in public hospitals with all their departments will be

examined.

Literature review

The literature review is a research about anything related to the subject which is bed

capacity. The purpose of the literature is to study and cover most possible information about the

topic. To combine or composite the information into conclusion, also to fill the gaps and question

marks that comes in mind. So, literature review is beneficial to know all the clues and have a good

documentation art about the subject. Also, the importance behind writing this literature review is

to do more research in journals and books about bed capacity to understand the reason of doing

study of bed capacity, how they solve the problem, and the method they follow. Healthcare system

it’s organization of people, institutions, and resources that cares about diagnoses. Also, provide for

the community patients the proper care. The goal of a healthcare system is to enhance the health

of the population by provide all resources and people need. Kuwait has provided great attention to

healthcare system. The healthcare in Kuwait considered as one of the first countries that support

healthcare. Also, it has many plans and projects to develop healthcare system in Kuwait. Moreover,

the healthcare in Kuwait consists of public and private sector and they provide health and medical

care. And there are 6 major hospitals that offer secondary healthcare.

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 8

Health care system and resources

Kuwait government has supplied social services of health care to the population. The

government has approximately spent 220 million KD annually on health care between 1986-1996.

This amount of money has improved the health care situation in general and national. Health care

has provided free public health care services to citizens and residents, although the increasing in

prices and population. The increasing of population required a policy to provide health care

services in order to allocate the resources continually for public health care system and the health

care system has increased eighteen-fold of expenditure from 1969-1970.

Health care system in Kuwait in public and private sector involves three levels: primary,

secondary and tertiary. The Primary level has rehabilitation, cure and prevention services in

specific health center. The Secondary level which provides cure service through special medical

department and clinics in general hospital. And tertiary level which has special medical care. In

the seventeen’s, Kuwait public health care consists of 70 general specific centers, 141 special

specific center, 6 public hospitals, one for each governate and 9 specialized hospitals, overall bed

capacity is 4425 beds. It has also 8 private hospitals and include 550 beds. (Burney N, Mohammad

Health care system contain healthcare resources which are the resource needed to

implement healthcare activities for example: workforce, facilities, revenue, equipment, and bed

capacity. These days, fairness in classification of healthcare resources and inequality have turned

real worries of health system in the world (Masoudi, abolhallaje, Raadabadi, Nazari, Salimi, &

Javani, 2015). World health organization says that a strong human resource can construct to

structure the evidence base to get ready for availability and accessibility of required health workers

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 9

in the right place, and desired quality. Moreover, it has been assessed that countries with lower

workforce which are less than 23 doctors and nurses generally fail to fulfill sufficient rates for

chosen essential healthcare interventions, as prioritized by the Millennium Development Goals.

(No publisher, 2009).

Bed capacity is very important because it is the essential resource in any hospital. we are

studying bed capacity because we to know why Kuwait want to increase the number of bed

capacity and if there is enough number of beds in each hospital. Also, many papers took about the

bed capacity. For example, there is a study done in Tehran about the inequality in distribution of

hospital bed. And they analyze it by the method of Gini coefficient and it is an amount with the

value between 0 and 1 which it means between minimum and maximum inequality. It is systematic

and independent of the mean. In addition, they have been used the method of Gini coefficient in

different studies in Iran and to estimate the degree of indexes, they use the number of beds per

population in each region. They clarify that while they are using the Gini coefficient between 2010

to 2012 the distribution of inequality of care bed had been increased. Also, (Masoudi, abolhallaje,

Raadabadi, Nazari, Salimi, & Javani, 2015). said if they continue using this method for the next

five years the trend of inequality distribution of intensive care beds in Iran will be extreme.

Moreover, they evaluated the inequality in the distribution of beds for the hemodialysis patients

and the result was there were no inequality for hemodialysis beds. On the other hand, they use the

method of Gini coefficient in college hospital beds in the Azarbaijan-gharbi and they found that

there was inequality in the distribution of hospital beds in the province. Gini coefficient and Lorenz

curve were determined. When the numerical estimation of the Gini index is somewhere in the

range of 0 and 1, where 0 illustrate perfect balance and 1 represent to inequality. When the index

is under than 0.2 complete balance is seen in the distribution. And if the value is between 0.2 and

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 10

0.3, moderate correspondence is seen in the distribution. The qualities between 0.3 and 0.4 shows

inequality in the distribution. When the estimation index between 0.4 and 0.6 show high inequality

in the distribution. The values greater than 0.6 demonstrate perfect inequality. The Gini coefficient

of the beds in 22 regions I Tehran in relation to the population in every region. So, the Gini

coefficient in 2010 was acquired to be 0.4666, in 2011 was 0.4658, and in 2012 was obtained to

be 0.4652. The Gini coefficient during the three years was 0.46. So, from this study the distribution

of beds in Tehran regions is not fair relative to the population. (Masoudi et al. 2015).

The hospital beds that are unused are seen as wasteful of scarce resource, thus the need to

show operational and financial efficiency for managers. However, when inadequate beds are given

to take care of demand, emergency patients will ‘board’ in the emergency department or spill over

into clinically inappropriate beds (Boulton, Akhtar, Shuaib & Bourke, 2016). While this may show

up operationally and financially efficient, from a patient point of view it might be harmful to their

care. (Boulton et al. 2016) discuss that waiting for a bed on a stroke unit following a stroke is

unacceptable.

The facts confirm that the demand for care and the capacity accessible to take care of that

demand shift significantly from market to market around the country (Wilson, 2003). In addition,

the issue of what level of capacity utilization is optimal has been discussed forever by the industry.

The most significant point is that it not possible for any hospital to operate at full capacity all of

the time. Rather, a hospital must form and staff for peak utilization point. The utilization is

different inside a hospital by day of the week, by month and by year, it is clear that a hospital must

set its optimal utilization level under 100%. Obviously, a community must strive to keep up bed

accessibility at a sufficiently high level to conform all sick patients in the area on the highest

volume day of the year (Wilson, 2003).

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 11

Smart hospital beds are extremely helpful for the patient and the healthcare professional

for the checking of vitals and different activities of the patient. Also, it keeps a track of the patient.

The smart beds have all significant kind of sensors which can monitor the movement, the pressure

of the patient laying, and non-invasively potions of the patient on the bed. In addition, smart beds

are equipped with the most recent innovation and LCD screen to check the active of the patient for

example, pressure, blood stream pattern, spinal movement direct to the doctor or the display

present on the bed. Moreover, the beds can show if it busy or available for the patient. Moreover,

hospital beds market is segmented into: North America, Europe, Latin America, Asia-Pacific, and

Middle East and Africa. (Smart Hospital Beds Market, No date).

Health care cost:

The amount of money that the government spend on health care is the health care cost. The

money is spent on the therapy and medical treatment. Having information about health care cost

to allocate the expenditure and to have new finance system. The healthcare cost information must

be managed to develop the healthcare services. There was a study of unit cost which is done in

Myanmar for the financial year 2015–2016 by choosing two public hospital Magway Teaching

Hospital (MTH) and Pyinmanar General Hospital (PMN GH), with the same number of beds (200

beds). From the study they conclude that the unit cost is affected by different elements like: the

efficiency of obtainable resources, the types of healthcare services provided, exploitation of

hospital services by the patients, and medical training of the physicians. According to BioMed

Central research for previous studies about cost analysis in India and South Africa to discover what

is the most thing that can influence the unit cost. In India and South Africa, the result was that the

human resource has the largest cost. Another study shows that the largest cost was for salaries and

then for drugs and consumables in Palestine in 2008. Back to the study done in Myanmar the

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 12

reform procedure that the government apply it to develop the health sector is too long “Myanmar

allocated 3.65% of its total budget on health in financial year 2016–2017 (850 million USD), which

was a nine-fold increase in absolute amount in financial year 2010–2011 (94 million USD)” (Than

et al. BMC Health Services Research, 2017). Even if government seems like it is working to

increase the budget of the healthcare sectors, the effectiveness of this increment is still

argumentative. The reason behind the study that has been done in the two hospitals that we

mentioned previously to do the healthcare cost analysis through a method with different steps:

• Study setting: they identify the name of the two hospitals that they have been

chosen for the study, the history of these hospitals, and why did they choose these

two hospitals.

• Data collection: they determine the duration for the data collection, from where

they took it, and what kind of data that they had collected.

• Costing method: identify the costing method that they applied for the study which

was step-down method that includes 7 steps: specify the final output, specify the

cost centers, specify the cost for every input, specify every input cost to cost

centers, allocation for every cost to the last cost centers, calculate the unit cost

,and finally write the report.

The result from this study was:

For PMN general hospital the occupancy rate for sanctioned beds was 83.35%, and for available

beds was 61.74%, the average number of the workers while doing the study was 232 per month.

For MTH the occupancy rate for sanctioned beds was 93.14%, and for available beds was 76.03%,

the average number of workers was 288 per month during the study. This what data shows in the

Figure1.

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 13

Figure 1 Data of MTH

The unit cost of the healthcare service analysis will include the unit cost per inpatient day, unit

cost per major inpatient wards, department of the outpatient, and theatre of operation. These are

shown in Figure 2, and Figure 3:

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 14

Figure 2 Unit cost of inpatient units’ schedule

Figure 3 Unit cost of outpatient schedule

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 15

It can be concluded that, the health care unit cost for the study that happened for 200 beds

in two of government hospital in Myanmar can be differ depending on different elements like

hospital service utilization, the resources that are valid for each cost center, and the medical service

type. Figure 4 shows different kind of cost components in the two hospitals. (Than et al. BMC

Health Services Research, 2017).

Figure 4 The cost variation of hospital components

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 16

It would be great to apply this kind of study for government in Kuwait for the healthcare sector to

know the budget need to provide good healthcare service. Also, to analyze the unit cost that will

help to improve health care management.

Healthcare spending is the consumption value of the healthcare system (the amount of

current health cost). In order to calculate this value, it is very important to look at a lot of things

like personal healthcare and collective service. For personal healthcare it includes medical goods,

rehabilitative care, long term care, curative care, and ancillary services. For the collective service

it is includes health administration service, prevention service, and public health service. Medicinal

services are financed through a blend of financing courses of action including government

spending, necessary medical coverage, the health insurance of the voluntary, and private finances.

Healthcare spending value is varied from country to country and it is depending on the ability of

Figure 5 Health spending

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 17

each country. Organization for Economic Co-operation and Development (OECD) calculated the

number of healthcare spending for different countries for year 2017 in USD per capita that will be

shown in Figure 5. (OECD,2017).

Analysis of bed capacity

Benefit of bed capacity

Bed occupancy rate is the measurement of the hospital ability to take care of its’ patients

properly. The measurement is useful for the hospital to manage bed capacity and the how well the

hospital serve the patient. The Irish Medical Organization, the Australian Medical association and

college for emergency medicine consider the occupancy rate which is more than 85% has bad

impact on the hospitals’ performance. As in health department in UK which it has more than 85%

occupancy rate, face difficulty in managing emergency and elective acceptance, so UK health

department has instituted 82% rate occupancy. There are several factors that effects the operational

target of the hospital bed occupancy quality measurement, these factors are: Risk of cross infection

between patient and inpatient, acceptance from emergency and risk for staff welfare (Keegan A D,

2010).

First, risk of cross infection in hospitals with high bed occupancy which is crowded hospital

will spread significantly on the contrary if the bed occupancy where low or on the target line.

Second, admission from emergency department, the hospitals that has average in bed occupancy

higher that others, risk their patient to delay the time for transferring them from emergency

department to inpatient bed. The National Health Services did a simulation study about the relation

between the patient need and the bed availability at the hospital. The study concludes that any

hospital has bed occupancy rate exceed the average which 85%, has failing in one of hospitals’

services. In 2005 the bed occupancy in Netherland was 64% and UK was 84%, Netherland was

PUBLIC HOSPITAL ANALYSIS OF BED CAPACITY IN KUWAIT 18

better in hospital services than UK. Finally, the last factor is the risk for staff welfare. The

overcrowded hospital will also impact on the staff infection, so there is relationship between bed

occupancy and the initiation of antidepressant therapy for the staff. The increasing of

antidepressant is corresponding to the occupancy rate. Finally, there is significant effects between

the occupancy rate of bed hospitals according to patient outcome from the hospital. (Hospital Bed

Occupancy, p 291-293)

Occupancy rate

## 2

1-1

Chapter 1
INTRODUCTION TO SIMULATION

Many problems addressed by current analysts have such a broad scope or are so complicated
that they resist a purely analytical model and solution. One technique for analyzing these
situations is simulation. Simulation is a technique to perform an experiment on an imitation of a
real world system in order to obtain data that can be used to make predictions about the system.
The range of applications of simulation is wide and can involve the use of physical models (e.g.
wind tunnels) or statistical models. A statistical model is one that takes random samples from
some probability distribution that describes the operation of some aspect of a system, or the total
system. Simulations that involve random sampling are usually referred to as Monte Carlo
simulations. Monte Carlo simulation is the only type of simulation that will be addressed in this
document, and the term simulation will refer only to this type.

Naval, and other operations, are often modeled for OA purposes using Monte Carlo
simulation. If the size of the sample is small and the model is simple, simulation may be done by
hand. More commonly it involves the use of a computer. In either case, it usually involves the
repetitive generation of artificial histories of several time periods during which the system is
operating, doing a statistical analysis of the data collected, and drawing inferences about the real
world system. Further classifications of simulation often involve how time, when it is a factor, is
treated in the simulation. If the treatment of time uses discrete steps, the simulation is called a
discrete-event simulation. Whenever something of significance (an event) happens in a discrete-
event simulation, the program determines the time in the “future” that the next event occurs and
the advances the clock to that time. If the treatment of time is as a continuous variable, then the
simulation is called a continuous-time simulation. The clock advance in a continuous-time
simulation may be in pre-defined jumps of a uniform size, or they may be determined by the
(usually numerical) solution of a differential equation. Sometimes time is handled in discrete
steps for some aspects of the simulation and in a continuous fashion for others. In this case, the
simulation is said to be a mixed simulation. This chapter will be limited to concepts that are
associated with the implementation of discrete-event simulations.

1.1 An Example

As an example of discrete-event simulation from queuing theory, consider a bank that has a
single drive-in window. Suppose that data were collected on the operation of the window and a
statistical analysis of the data indicated that the distribution of the time between customer
arrivals and the distribution of the time to serve a customer are as given in Table 1.1.

1-2 INTRODUCTION TO SIMULATION

Table 1.1: Input Distributions

Time between arrivals (min) 1 2 3 4 5
Probability 0.1 0.1 0.3 0.3 0.2

Service time (min) 2 3 4 5

Probability 0.4 0.3 0.2 0.1

A simulation to investigate the time the customers spend at the bank (waiting in line and being
served) is desired.
In order to simulate the operation of the drive-in window, one needs the time of arrival of
each customer and how long the service of each customer takes. If there are no customers at the
beginning of the simulation, the arrival of the first customer can usually be assumed to occur at a
time (after the beginning of the simulation) that has the same distribution as the time between
arrivals. Sometimes the simulation begins with the arrival of the first customer, and sometimes a
separate distribution is needed for the arrival of the first customer. In this example, the time to
arrival, from time zero, of the first customer will be assumed to have the same distribution as the
time between arrivals.

In order to sample from a distribution, some method of generating a random number is
usually used. A random number is an observed value of a random variable that has a uniform
distribution on the interval from 0 to 1 (unif(0, 1)). Random numbers may be obtained from a
mechanical device, from a table of random digits, or from a random number generator on a
calculator or a computer.

For the generation of the arrival times of the customers at the drive-in window, suppose that
10 cards are available that are numbered 1 through 10. The cards are shuffled, and one is drawn
at random. The number of the card drawn would be used to determine the simulated time
between arrivals of customers at the bank. For example, if the card is a 9 or 10, then the time
between arrivals is taken to be 5 minutes. Since drawing 2 of the 10 cards results in a time of 5
minute, this should give a probability of 0.2 for an interarrival time of 5 minutes. The card
number and the associated simulated time between arrivals are as follows:

Table 1.2: Card Values for Time Between Arrivals Distribution

Card number 1 2 3, 4, 5 6, 7, 8 9, 10
Time between arrivals (min) 1 2 3 4 5

Suppose that the first card drawn is numbered 10. Then the arrival of the first simulated
customer would occur at time equal to 5 minutes. That card is then replaced in the deck, the deck
is shuffled, and a second card is drawn at random. Suppose the second card drawn is numbered
8. This would then give 4 minutes as the time between the arrivals of the first and second
customer. The time that the second customer arrives is then at 5 + 4 = 9 minutes. The time

SIMULATION NOTES

1-3

between the arrivals of customers two and three is found by shuffling the 10 cards and selecting
a third card at random. Suppose that the third card drawn is a 5, giving a time between arrivals of
3 minutes. Adding this to the time of arrival of the second customer yields the time of arrival of
the third customer at 12 minutes.

A similar procedure can be used to generate the service times of each of the three
customers. Using the same deck of cards, suppose that three random draws of cards yielded cards
numbered 1, 9, and 2. Using the following table, which was constructed from the original
probability distribution of service times, the service times of the three customers are simulated as
2, 4, and 2 minutes:

Table 1.3: Card Values for Service Time Distribution

Card number 1, 2, 3, 4 5, 6, 7 8, 9 10
Service time (min) 2 3 4 5

In order to find the total time each customer spends at the bank, one needs to determine the
time the customer arrives, the time the customer begins service, and the time the customer ends
service. The total time is then the difference between the customer’s arrival time and the time
service ends. The first customer arrives and begins service at time 5 minutes. The service time
for the first customer is 2 minutes, and departure occurs at time 7 minutes. The total time the first
customer spends at the bank is 2 minutes. The second customer arrives at time 9 minutes and,
since the first customer has already departed, service begins immediately. This service takes 4
minutes, and departure is at time 13 minutes. The time the second customer spends at the bank is
then 4 minutes. The third customer arrives at time 12 minutes and begins service at time 13
minutes, when the second customer departs. Service for the third customer takes 2 minutes and
departure occurs at time 15 minutes. The total time the third customer spends at the bank is then
15 – 12 = 3 minutes.

An aid in handling simulations done by hand is the use of a table to organize the operation.
For the bank’s drive-in window, the table might be as given in Table 1.4.

Table 1.4: Hand Simulation of Three Customers

n

Card
no.

Between
arrivals
(min)

Arrival
(min)

Begin
service
(min)

Card
no.

Service
time
(min)

Departure
time
(min)

Total
time
(min)

1
2
3

10
8
5

5
4
3

5
9
12

5
9
13

1
9
2

2
4
2

7
13
15

2
4
3

1-4 INTRODUCTION TO SIMULATION

A problem with doing a simulation by hand, is that it is time consuming and tedious to
generate enough data to be statistically significant. The construction of the above table can be
done using a spreadsheet and the copy/paste options allow the quick generation of large data sets.
The first thing to address in generating such a table could be the selection of times between
arrivals and service times in some “random” fashion. Spreadsheets have a built-in “random
number” function that may be used. The function in Microsoft Excel is RAND(), which returns a
number between 0 and 1. A process for doing this and some of the properties such a “random
number generator” must satisfy will be addressed later.

In order to convert a (random) number between 0 and 1 to the appropriate time needed in
our example, we will use a look-up function defined in spreadsheets. The function is defined by
putting 𝑥 and 𝑦 values in a table. The table may either be a vertical table, with the 𝑥 and 𝑦 values
in columns, or a horizontal table, with the values in rows. The 𝑥 values should consist of the
cumulative distribution values, beginning with 0 and ending with 1 (see the tables below). The
corresponding 𝑦 values are the times to use whenever the generated random number is greater
than or equal to the 𝑥 value, but less than the following 𝑥 value. For example, the arrival time
table given below has 0 as the first 𝑥 value and 0.1 as the second. The first 𝑦 value is 1, so if the
random number generated is between 0 and 0.1, the value of 1 will be returned. Similarly, if the
value of the random number is between 0.5 and 0.8, the value 4 will be returned. The format for
the vertical lookup table in Excel is

VLOOKUP(value, table, column).
For example, the entry in cell B14 of the spreadsheet might be =RAND(), generating a random
number, and the entry in cell C14 might be =VLOOKUP(B14,\$A\$4..\$B\$9,2), which returns the
value corresponding to the random number in the arrival time table. Notice that the table cell
references have been fixed, as indicated by the \$ signs. This may be easily done using the F4 key
when the cell references are selected. The values of the random variable will be recalculated each
time the spreadsheet is updated. Once the spreadsheet is completed, a different simulation may
be obtained simply by pressing the F9 key. The automatic recalculation may be stopped by
selecting Options under the Tools menu, selecting the Calculation tab, and then changing the
selection to Manual. The notebook will not be recalculated then unless the user presses the F9
key.

SIMULATION NOTES

1-5

Table 1.5: Input Distributions in a Spreadsheet Format

The two tables are given names to make referring to them much easier. This is done for the
time between arrivals table by selecting cells A4 through B9 and typing the name in the cell
name box just above column A as shown in Table 1.5a. The name ‘TBA’ is assigned to A4..B9
and the name ‘ServiceTime’ is assigned to the cells D4..E8. These names will be available for
use whenever reference is made to one of the tables.

Table 1.5a: Assign Name to Cell Range

The table for the simulation may now be easily built. Rows 1, 2, 3 and 4 of Sheet2 are used
for column headings as shown in Table 1.6. Column A will be used to count the number of
customers. Thus the first formula row is 5. This first row will be different from the remainder of
the table due to references to cells that do not exist for this row. The formula in A5 is =1, while
the one in A6 is =1+A4. Since there is no number in A4, a reference to this cell may result in an
error unless the cell is completely empty. The entry in B5 is =RAND(), the random number
generator, as it will be for the remainder of the table in column B. The entry in C5 also contains
no missing cell references, so it is =VLOOKUP(B5,TBA,2), the vertical table lookup function,

1-6 INTRODUCTION TO SIMULATION

and will be valid through the remainder of the column. The time of arrival, D5, is calculated as
the time the previous customer arrived plus the time between arrivals (interarrival time). Thus
the entry in cell D5 is =C5, while it is =D5+C6 in cell D5.

The begin service time is a bit more complicated, since a customer must wait until the
previous customer leaves before service can begin as there is only one server in this system.
Thus the time a customer begins service, column E, is the larger of the time the previous
customer departs (previous row of column H) and the time the customer arrives (same row of
column D). The entry in E5 could then be =D5, while the one in E6 would be =MAX(H5,D6).

Columns F and G are used to generate service times similar to columns B and C. The
departure time is then the begin service time plus the service time, so the entry in H5 would be
=E5+G5. Finally, the total time the customer spends in the system is calculated as departure time
minus arrival time. Thus the entry in I5 would be =H5-D5. Columns F – I of row 5 should now
be selected, copied, and pasted to complete row 6. The entire row 6 can then be copied and
pasted to obtain a simulation of multiple customers. The table below shows only 7 customers.

Table 1.6: Simulation Example Using Spreadsheet

If the simulation of 1 day is desired, the conditional function may be used. For example, D6
could be modified to read =IF(D5+C6<480,D5+C6,” “) which will leave the cell blank if the
time exceeds 8 × 60 = 480 minutes.

1.3 Performance Measures
There are two basic types of averages that are often used in comparing alternate systems,

especially if they involve a queue. The first is the average or mean of a function of a discrete
variable, the second is the average of a function of a continuous variable (often time).

SIMULATION NOTES

1-7

For an example of the average of a function of a discrete variable, we might be interested in
the average time the first 5 customers spend at the drive-in bank. A particular simulation of the
bank might yield 4, 2, 3, 3, and 2 for the times, in minutes, that the first five customers spend in
at the bank. The average time the five customers spend at the bank is

𝑊 =
4 + 2 + 3 + 3 + 3

5
=
14
5
= 2.8.

For an example of the average of a function of a continuous variable, we might be interested
in the average number of customers at the bank at any time. This is also called the time average
number of customers. In order to find this quantity, we may construct the function 𝑁(𝑡), the
number of customers at the bank at time 𝑡 (minutes after the bank opens). One way to do this is
to arrange the events at the bank in chronological order. In a spreadsheet, this may be
accomplished by copying the arrival events and the departure events into the same column, with
their corresponding times in an adjacent column, and then sort on the time. The resulting table,
covering the time until the departure of the fifth customer, might look like the following table.

Table 1.7: Number of Customers in Bank

time t event N(t)
0 begin simulation 0
4 arrival 1
8 arrival 2
8 departure 1

10 departure 0
11 arrival 1
14 departure 0
15 arrival 1
18 departure 0
19 arrival 1
20 arrival 2
21 departure 1

Notice that the sixth customer arrived before the fifth customer departed. This will affect the
average value of 𝑁(𝑡), and must be included in our calculations. The graph of the function is
given in Figure 1.1 below.

The average value of 𝑁(𝑡) over the interval [0,𝑇] is defined as

𝐿 =
𝑁(𝑡)  𝑑𝑡!!
𝑇

.

In this case, the value of the integral of 𝑁(𝑡) over the interval [0, 21] can easily be found to be
15 by adding the area of the rectangles in the graph. Thus 𝐿 = 15 21 ≈ 0.71.

1-8 INTRODUCTION TO SIMULATION

Figure 1.1: Graph of Number of Customers in System

Although the method of calculating the average of 𝑁(𝑡) given above is conceptually correct,
it is difficult to automate on a spreadsheet. However, this may be overcome with a clever
argument. Note that each of the first 5 customers contribute an area equal to the time they spend
at the bank, for a total of 14. The sixth customer then contributes an area equal to the time she
spends at the bank prior to the end of the interval [0, 21]. This again yields the estimate of
(14 + 1)/21 = 15/21 for the average number of customers at the bank. This method of
calculating the integral is then no harder than adding the proper times, as was done in for the
average time at the bank. The right most column of Table 1.6 shows how this can be
implemented in a spreadsheet. To get the value in column J, find the time between when the
customer arrives and when the 5th customer departs and take the minimum of this number and
the total system time for the customer. This is the value that goes into column J, provided it is
positive. A formula for doing this in the 10th row of column J is =MAX(0,MIN(H10-D10,21-
D10)).

A third performance measure that is useful in queuing models is the server utilization, 𝜌. The
server utilization is defined as the proportion of time that the server is busy serving a customer.
This can be found by dividing the total service time by the total time. For the example above, the
teller is busy for 14 minutes out of the total 21 minutes. Thus the server utilization is 𝜌 = 14/21

1.4 Standard Error

A common performance measure used in studies involving simulation is the expected value
(or mean) of a random variable that occurs in the system. In the bank drive-in window example
above, the expected time a customer spends at the bank, the expected number of customers at the
bank at any time, and the server utilization are all of this nature. Since the bank has a natural

14

1

2

2

16

3

4 206 228 1810 12

N(t )

t

1

2 3 34 2

SIMULATION NOTES

1-9

starting and ending time (one day) and a natural starting state (no customers in the bank when it
opens), one approach to estimating the expected time a customer spends in the bank would be to
(i) replicate 𝑛 simulations of one day’s operation of the bank, (ii) average the times spent in the
bank by each customer during a day’s simulation (obtaining one estimate per day), and then (iii)
use the 𝑛 estimates obtained to find both a point estimate (the average of the 𝑛 estimates) and an
interval estimate (explained below) of the expected time a customer spends in the bank. Note
that the time an individual customer spends in the bank on a given day will be correlated to the
times spent in the bank by the preceding customers. For this reason, only one estimate (the
average) is obtained from each day’s simulation. If different random numbers are used in each
day’s simulation, the 𝑛 estimates of the average time a customer spends in the bank should be
independent and identically distributed. In that case, the following discussion applies.

Suppose that the mean, E[𝑋], of a certain random variable 𝑋 is to be estimated using
simulation. If the simulation is performed 𝑛 times and 𝑛 estimates, 𝑥!,… ,𝑥!, are obtained, then a
point estimate of E[𝑋] is the sample mean,

𝑥̅ =
1
𝑛

𝑥!

!

!!!

.

Each of the sample values, 𝑥!, is a random variable having the same (usually unknown)
distribution with mean E[𝑋] and variance 𝜎!. The sample mean, 𝑥, is a random variable with
mean E[𝑋], since

E 𝑥 =
1
𝑛

E 𝑥!

!

!!!

=
1
𝑛

E[𝑋]
!

!!!

=
1
𝑛
𝑛E 𝑋 = E 𝑋 .

Similarly, assuming that the xi are statistically independent, the variance of 𝑥  is

Var 𝑥 =
1
𝑛

!

Var[𝑥!]
!

!!!

=
𝜎!

𝑛
.

The assumption of independence is usually valid whenever the estimates are taken from different
replications of the model, the random number streams used are non-overlapping, and the initial
conditions are independently chosen. It would not ordinarily be valid if, for example, the
estimates were a sequence of output observations from a single replication of the model. Thus in
the simulation of the bank’s drive-in window, using the average of the times spent at the window
by all customers during a day’s simulation would be acceptable, while using an individual time
spent at the window by a customer would not.

An unbiased estimate of 𝜎!  is the sample variance

𝑠! =
1

𝑛 − 1
𝑥! − 𝑥 !

!

!!!

.

The corresponding estimate of Var 𝑥 can then be found. The resulting estimate of the standard
deviation of the sample mean, 𝑥, called the standard error and denoted 𝑠𝑒(𝑥), can then be

1-10 INTRODUCTION TO SIMULATION

found by dividing the sample standard deviation by the square root of the sample size,

𝑠𝑒 𝑥 =
𝑠
𝑛
.

The standard error is a measure of the accuracy of the estimation of E[𝑋]. Note that the sample
size must be multiplied by 100 in order to reduce the standard error to one tenth its earlier value.

If 𝑥 is approximately normally distributed, then the standard error may be used to obtain an
interval estimate (called a confidence interval) for E[𝑋]. For 0 ≤ 𝛼 ≤ 1, a 𝟏 − 𝜶 ⋅ 𝟏𝟎𝟎%
confidence interval for E[𝑿] is given by

𝑥 − 𝑡!/!,!!! ⋅ 𝑠𝑒 𝑥 ≤ E 𝑋 ≤ 𝑥 + 𝑡!/!,!!! ⋅ 𝑠𝑒(𝑥)

where 𝑡!/!,!!! is the value for a student’s 𝑡 random variable with 𝑛 − 1 degrees of freedom. In
Excel, it is given by TINV(𝜶, n − 1) and Excel automatically divides the 𝛼 by 2.

The sample mean 𝑥 is normally distributed if x is normally distributed or, by the Central
Limit Theorem, it is approximately normally distributed when the sample size 𝑛 is large; in
practice 𝑛 larger than 30 is adequate. For smaller values of 𝑛, a statistics book must be consulted
for ways to obtain a confidence internal for E[𝑋]. The 1 − 𝛼 ⋅ 100% confidence interval is the
interval centered at the (point) estimate 𝑥̅ that would be expected to contain the actual mean in
1 − 𝛼 ⋅ 100%  of the cases when the sample experiment (i.e. 𝑛 replications of the simulation) is

repeated many times. Of course, only one sample experiment is ordinarily taken, and there is no
way to know whether or not the actual value of the parameter being estimated is really in the
confidence interval.

The standard error and resulting confidence interval may be useful in deciding how many
estimates must be obtained in order to achieve a desired accuracy. The simulation is usually first
done a few times in order to obtain an estimate of the size of sample variance. This estimate is
then used to solve for the value of 𝑛 that should give values close to a desired level of accuracy.
For example, suppose that an estimate within 0.1 of E[𝑋] was desired at a confidence level of
95%. Whenever 𝑛 is large, the student’s 𝑡 distribution and the standard normal distribution, 𝑧,
are very close, so we use the standard normal distribution in this case to simplify the procedure.
With 𝛼 = 0.05 the value for 𝑧 is 1.96. Suppose an initial sample of 30 replications of the model
was made to compute a sample variance for the purpose of determining the number of
replications required to estimate E[𝑋] to the desired accuracy. Suppose the sample variance was
found to be 3.2. Then,

1.96 3.2
𝑛

= 0.1

can be solved for 𝑛 as (1.96 × 1.79 / 0.1)2 = 1229.3. Since the number of replications must be an
integer, the estimate for the number of replications needed would be 1230, to estimate the actual
value of E[𝑋] within 0.1, 95% of the time. Of course the actual number of replications needed
may vary from this estimate, since the variance may be substantially larger than the estimate
used.

SIMULATION NOTES

1-11

1.5 Replications using Excel
Excel has a built-in tool that allows multiple replications of a simulation. It may be found in

the Data menu and is named Tables. Before using this tool, we first add lines to our simulation
so that one day’s (8 hours’) operation of the bank is simulated. This is shown in Table 1.9. In
addition to the added lines, the length of the simulation was added (column K) and the formulas
in columns I and J were modified to use this end time. The new formulas are shown in Table 1.9.
Making a cell entry ‘na’ means that those cells will not be used in the average calculation. If we
had put zero in the cell, they would have been used in the average calculation, making it smaller
that the desired value, in most cases. Zeros in column J would be fine because they do not affect
the SUM function. Blanks would have worked just as well.

Table 1.9: Simulation for One Day

We are now ready to have Excel do replications for us. The first step is to create a table to
contain the results. This may be done on the same sheet as the simulation or on a separate sheet
as shown in Table 1.10. The first column contains an index showing the number of replications
desired. The first line in the second column contains the value of the average waiting time in the
system, 𝑊, (cell I157 on the table1_9 spreadsheet). The first line in the third column contains
the value of the time average number of customers in the system, 𝐿, (cell I158 on the table1_9
spreadsheet). We wish to collect the values of 𝑊 and 𝐿 for 30 replications of the simulation. We
select the 30 rows and 3 columns where the values are to be placed. Then we open the Data
as shown in Table 1.10. This opens the dialog box shown in Figure 1.2. We are constructing a

1-12 INTRODUCTION TO SIMULATION

one dimensional table based on the columns, so the Row input cell is left blank and the Column
input cell contains a reference to the first column in the table, \$A\$3. Clicking the OK button
causes Excel to recalculate the simulation 30 times and fill the values in each of the two columns
based on the values in the cells indicated. The results are shown in Table 1.11.

Table 1.10: Begin Replications of Drive-In Teller Simulation

Figure 1.2: Table Dialog Box

SIMULATION NOTES

1-13

Table 1.11: Completed Table of Replication Values

Next we wish to obtain 90% confidence intervals for 𝑊 and 𝐿 based on these observations.
We use the AVERAGE() and the STDEV() functions in Excel to calculate the values needed for
the sample average, 𝑥̅, and the sample standard deviation, 𝑠. The value of 𝛼 is 1 − 0.90 = 0.10
and the degrees of freedom is 𝑛 − 1 = 29. To find the critical 𝑡-value, we use the TINV()
function in Excel. This function gives the two-tailed probability for the 𝑡 distribution, so we do
not divide 𝛼 by 2. The correct syntax to get the value of 𝑡!/!,!!!  is TINV(𝜶,𝒏 − 𝟏). These
calculations, as well as those for the standard error, the precision, the lower confidence level and
the upper confidence level, are shown in Table 1.12. Our results are that an estimate of the
average time a customer spends in the system is 4.8 minutes, with a 90% confidence interval of
4.5 to 5.1 minutes. The estimate for the average number of customers in the system at any time is
1.4 customers, with a 90% confidence interval of 1.3 to 1.5 customers.

1.6 Steps in a Simulation Study

Most studies that involve simulation pass through the same sequence of steps. Most of these
steps are also used in types of analytical studies that use other modeling techniques. Figure 1.3
below illustrates how the steps usually proceed. Of course they do not always follow in the order
given, and sometimes the analyst must return to a previous step to make modifications to the
model.

1-14 INTRODUCTION TO SIMULATION

Table 1.12: 90% Confidence Intervals Calculations

1. Problem Identification. The first step in any study is the realization that there is a problem.
Often the source of the problem is a decision maker who tasks the analyst with providing insight
so that an informed decision can be made. The analyst must be careful to verify that the nature of
the problem is clearly understood, and agreed upon. An elegant solution to the wrong problem is
beneficial to neither party.

2. Problem Formulation. It is crucial that the analyst make a formal statement of the problem,
as he/she understands it, that contains as much detail as possible. The problem statement should
then be verified by the decision maker to help assure that there is agreement as to the nature of
the study. As the analysis progresses, the formulation of the problem may change as its nature is
better understood. The awareness of the existence of a problem may often come long before the
knowledge of the nature of the problem. The analyst will be wise to make a careful statement of
the problem, to obtain verification from the decision maker, and to keep the decision maker
informed of any reformulation of the problem that may arise.
3. Goals. There is a saying to the effect that “one who aims at nothing will surely hit it.” The
analyst who takes the time to think about what must be done to solve the problem will have a
better chance of providing the decision maker with useful analysis. The setting of goals or
objectives that are needed will serve as a kind of road map for the journey. Of course these goals
will probably have to be modified along the way, but they can serve to keep the study focused
and to keep the objective clearly in mind.
4a. Model Outline. The formulation of the problem often indicates to the analyst that a specific
tool may be useful in the study. If the problem is very complex and/or analytical solutions are
unknown, simulation may be the tool of choice. If this is the case, the analyst must have a
“picture” of the system to be modeled. This picture may be obtained by observing the system to
be modeled in action and/or discussing the system with knowledgeable experts. A diagram or

SIMULATION NOTES

1-15

flow chart of the model visualized may be extremely beneficial. The analyst must begin to decide
which of the elements of the system are to be included in the model, and which elements are to
be left out of the model.
4b. Data. As part of learning about the system, and for input to the model, data collected from
the system must be obtained and analyzed. This may be done in conjunction with building the
model outline. In fact, collecting the necessary data and observing the system in action may be
accomplished in tandem. The analysis of the data should also provide insights into the model
outline.

5. Coding. Translating the visualized model into the language of the software used is often
called coding. This is because simulation models were first written completely in high level
languages such as FORTRAN. Depending on the nature of the study, the analyst may be able to
make use of a more modern simulation environment, such as ProModel. More complicated
simulations for specific purposes are often written in C or C++.
6. Verification. Du

## 2

IE300 Industrial Engineering Seminar
Assessment – 3 (15 %) – Spring 2022

Mid-Semester Report (Problem Statement and Background)
Due by Monday 18th of April 2022

Project Title: Estimating Delivery Staffing Needs in a Fast Food Restaurant Chain using

Monte Carlo Simulation

and the problem statement and objectives. Also include your literature review

Use the GP I Final Report Writing Template posted at the Industrial Engineering Seminar Moodle page
by Dr. Suat Kasab, prepare this mid-semester report for your graduation project.

Note that this report will be a group work and you need to submit one report to Turnitin on your G24

You have already conducted a literature review for your project topic (on Monte Carlo Simulation

and its applications). Building on that, develop your problem statement and project objectives. You

assignment. You need to the knowledge you have gained based on the readings in a single part.

The goal of this report in demonstrate your vision of the project by in well-defined and supported

problem statement and objectives to be achieved.

The problem statement should be a focused paragraph presenting the core task that you will work

on in the project. The project objectives are a few statements stating what you will present at the

end of the project.

Use the template provided to you by the graduation project coordinator for the formatting. You can
use font size of 11, Calibri style, and line spacing of 1.5 lines. Page margins of 1 inch in each side is
recommended. Do not exceed 15 pages of the main report body and use appendices in a smart way if
needed.

Benefit from the suggested report contents that we discussed in our meeting.

## 2

Course Syllabus

Course Description

Explores strategies for leading and communicating effectively with both internal and external audiences during crisis
situations. Discusses the development of a communication plan and how to craft and deliver messaging during the crisis
situation.

Course Textbook(s)

Ulmer, R. R., Sellnow, T. L, & Seeger, M. W. (2019). Effective crisis communication: Moving from crisis to opportunity (4th
ed.). SAGE. https://online.vitalsource.com/#/books/9781506315744

Course Learning Outcomes

Upon completion of this course, students should be able to:

1. Apply crisis communication theory to real-world crisis situations.
2. Evaluate leaders’ approaches to crisis communication and action.
3. Apply strategies for communicating and leading during times of uncertainty.
4. Apply strategies for communicating a message to neutralize risk or scandal.
5. Create opportunities for positive messaging in the midst of crisis, in order to support the organization, its people, and

its brand.
6. Evaluate ethical demands of the leader during crisis situations.
7. Create a leadership communication plan for a crisis situation.
8. Develop strategies for leading the organization toward crisis recovery and renewal.

Honesty and integrity are taken very seriously at Waldorf University. All students should be familiar with the Waldorf
University Academic Integrity Policy (found in the current Student Handbook) and the consequences that will result from
breaches of this policy.

Credits

Upon completion of this course, the students will earn 3.00 hours of college credit.

Course Structure

COM 5360, Crisis

COM 5360, Crisis Communication and Leadership 1

1. Study Guide: Course units contain a Study Guide that provides students with the learning outcomes, unit lesson,
required unit resources, assignments, and supplemental resources.

2. Learning Outcomes: Each unit contains Learning Outcomes that specify the measurable skills and knowledge
students should gain upon completion of the unit.

3. Unit Lesson: Unit Lessons, which are located in the Study Guide, discuss lesson material.
4. Required Unit Resources: Units contain Required Unit Resources from one or more chapters from the textbook

and/or outside resources.
5. Discussion Boards: Students are required to submit Discussion Board posts in Units I-VIII. Discussion Boards

provide students the opportunity for student-to-student and professor-to-student interaction based on relevant course
concepts and ideas. Specific information about accessing the Discussion Board rubric is provided below.

6. Unit Assignments: Students are required to submit for grading Unit Assignments. Specific information and
instructions regarding these assignments are provided below. Grading rubrics are included with each assignment.
Specific information about accessing these rubrics is provided below.

7. Ask the Professor: This communication forum provides students with an opportunity to ask their professor general
questions or questions related to course content.

8. Student Break Room: This communication forum allows for casual conversation with other classmates.

Unit Assignments

Unit I Assignment

Conduct a search of news reports that involve an organization responding to crisis events. Search for a range of reports to
get an overview of the types of crises that organizations have responded to in recent years. Then, select one crisis event to
develop your paper, addressing the following points. Support your response with specific examples from the news report
and our assigned readings, and illustrate the specific course concepts you relied on to draw your conclusions.

Define organizational crisis, and explain the difference between risk and crisis.
Describe the criteria leaders should use to determine whether an event constitutes a crisis event.
Who were the stakeholders? Who was impacted by the crisis—both inside and outside of the company?
Was the crisis preventable?
Were the circumstances of the crisis predictable/unpredictable? Were there elements of uncertainty that were outside of
What can the organizational leaders learn from the crisis and their responses?
Who spoke to the media/public on behalf of the organization? What message did he or she convey on behalf of the
organization (i.e., did he or she seek to support stakeholders, assign/accept blame for the crisis, communicate the
organization’s plan for recovery)?
How could the organization make the response more effective?

See the grading rubric for additional guidelines. It is recommended that you use the rubric as a checklist as you draft the
essay. Refer to the rubric often, and be sure to fulfill the requirements for all criteria listed.

Your paper must be at least two pages in length. Adhere to APA Style when constructing this assignment, including in-text
citations and references for all sources that are used. Please note that no abstract is needed.

This formal paper example provided by the Waldorf University Writing Center shows this type of formatting.

Unit II Case Study

After reviewing the case described in Example 4.3 on pages 57-60 of your textbook, write an analysis using discourse of
renewal theory as a framework to analyze the organization’s crisis response. Using the Waldorf Online Library, conduct any
additional research necessary to fully evaluate the aspects of the crisis response described in the theory. Cite specific

See the grading rubric for additional guidelines. It is recommended that you use the rubric as a checklist as you draft the
essay. Refer to the rubric often and be sure to fulfill the requirements for all criteria listed.

Your case study must be at least two pages in length. Adhere to APA Style when constructing this assignment, including in-
text citations and references for all sources that are used. Please note that no abstract is needed.

This formal paper example provided by the Waldorf University Writing Center shows this type of formatting.

COM 5360, Crisis Communication and Leadership 2

Unit III Case Study

After reviewing the case described in Example 4.6 on pages 68-72 of your textbook, write an analysis by responding to the
questions listed in the table under “You Make the Call” on pages 71-72 named “Lessons on Producing Effective Crisis
Communication”. After answering these questions, also write a brief analysis on Dominos’ organizational leader’s goals
during their crisis response.

Present your responses in a format you would use if you had been hired by Domino’s as a crisis communication consultant
and were preparing this report to provide to the client directly. Ensure the content, tone, and presentation are appropriate for

See the grading rubric for additional guidelines. It is recommended that you use the rubric as a checklist as you draft the
analysis. Refer to the rubric often, and be sure to fulfill the requirements for all criteria listed.

Your paper must be at least three pages in length. Adhere to APA Style when creating citations and references for this
assignment. APA formatting, however, is not necessary

Unit IV Assignment

This assignment has two components – an outline and a code of ethics. Please prepare both portions and submit as one
single Word document. Use section headings to organize the information, but do not paste the assignment instructions into

Part I: Introduction and Outline

The final project in this course is to create a crisis communication plan. From within the course syllabus, review the
assignment instructions for the final project. Approach the project as if you are the director of communications for an
organization, which can be a for-profit or non-profit organization.

Please use complete sentences within the outline/introduction and be sure your outline/introduction applies course
concepts. Draft the outline/introduction by performing the following actions:

Describe the industry/organization you are representing.
List the stakeholders (specific customers, clients, shareholders, and other groups) that your organization serves and/or
impacts.
Explain any concerns or challenges the organization might face, including potential risks, previous crises, or other issues
that will need to be considered when you develop the crisis communication plan.
Find an existing crisis communication plan for a similar organization, and link to the document. Identify at least two
lessons described in Chapter 3 that are followed in the plan.
Discuss whether or not any lessons are evident in the plan and the impact, if any, on the effectiveness of the plan.

Part II: Code of Ethics

Create a code of ethics for leaders responding to crisis events. The code must

have at least 10 original, ethical guideline statements,
include statements that are written in complete sentences (For example, accountability is a guiding principle, but it is not
a specific guideline. Instead, an ethical guideline based on the principle of accountability might be, “We will publicly
acknowledge errors in production, policy, or judgment that harmed stakeholders.”), and
include guidelines that demonstrate you are applying course concepts.

For examples of codes of ethics, you can conduct a search for policies from organizations and industry associations like
the one you have selected for the project. Be sure to review the codes only to familiarize yourself with the types of
statements that are included and the overall format.

To complete the assignment, you must write original guidelines. Ensure that you do not plagiarize another policy by using
guidelines contained in existing codes.

See the grading rubric for additional guidelines. It is recommended that you use the rubric as a checklist as you draft the
code of ethics. Refer to the rubric often and be sure to fulfill the requirements for all criteria listed.

Your introduction, outline, and code of ethics all together in one document must be at least three pages in length. Adhere to
APA Style when creating citations and references for this assignment. APA formatting, however, is not necessary

COM 5360, Crisis Communication and Leadership 3

Unit V Assignment

Press Release

Review Example 6.4 on pages 98-101 of your textbook. Assuming the role of the public relations director for King Car,
create a press release in response to the second round of testing that came back positive for high levels of melamine.

The press release must

show you relied on the 10 lessons in Chapter 5 as a guide to develop the content of the press release,
include any relevant information described in the case study (conduct additional research on the case as needed),
include at least one quote from a King Car representative (attribute the quote to yourself as the PR director for King
Car).

Your press release must be at least one page, but no longer than two pages in length. Adhere to APA Style when creating
citations and references for this assignment. APA formatting, however, is not necessary.

You can conduct a search for press releases to use as examples. Review the press releases only only to familiarize
yourself with the structure and overall format. To complete the assignment, you must write an original press release.

Ensure you do not plagiarize another press release by using content in any example press releases. (For more information
Programs Catalog.

Unit VI PowerPoint Presentation

PowerPoint Presentation

Review Example 4.1 on pages 49-53 of your textbook. Using the 10 lessons in Chapter 7 as a guide, assume the role of a
crisis communications consultant hired by BP one month after the spill has been contained. Develop a PowerPoint
presentation for BP leadership to use during a press conference that will be given within the next week, with the purpose of
employing positive messaging, repairing the company’s image, and explaining the company’s future plans.

The presentation must be at least eight slides, not including the introduction or citation slide. Use image repair theory
(described in Chapter 2) as a framework for your approach.

When using images in a public presentation, you can use any of your own original images for which you own the copyright
(such as photos you took yourself). If you search for images online, keep in mind that some photos might not be public
domain (i.e., free to use). They could have a copyright that requires either permission or purchase to use. To avoid copyright
infringement, it is best to use photos that you can clearly identify as public domain. Free stock photos (which are public
domain photos and do not have a copyright) are available at http://www.freeimages.com/.

Unit VII Assignment

Social Media Policy

Create a social media policy for an organization (of your choice) with the goal of positive messaging, neutralizing risk, and
crisis prevention. Select the same organization as for the final project (creating a crisis communication plan). This social
media policy will be incorporated into the final project as one section of the entire crisis communication plan. The format
should follow the same format used in the crisis communication plan.

clearly identify the organization/target audience that the social media policy is written for.
describe procedures regarding how employees (such as the PR director/spokesperson) should use social media when
representing the organization. Explain how social media can be used for positive messaging, crisis prevention, and
neutralizing risk. Add any other sections that might be relevant to your organization. Apply course concepts when you
create the policy.
include clear, detailed procedures using a format that is easy to follow.
use text enhancements and visuals to emphasize and for clarity. In addition to basic enhancements, such as bold,
underline, italics, caps, font/font size, and color-coding, you can include graphs, illustrations, or other visual elements.

COM 5360, Crisis Communication and Leadership 4

You can refer to examples of crisis communication plans to determine a format for the policy. Review these plans ONLY to
familiarize yourself with the structure and overall format. To complete the assignment, you must write an original policy.
Ensure you do not plagiarize another policy by using content in any example social media policies or crisis communication
plans.

Your policy must be at least three pages in length. Adhere to APA Style when creating citations and references for this
assignment. APA formatting, however, is not necessary

Unit VIII Final Project

Crisis Communication Plan

Create a crisis communication plan for leaders in a specific organization.

The plan must

clearly identify the organization/target audience the plan is written for,
create sections describing each type of potential crisis this organization might encounter and an appropriate response,

The sections should be tailored to your specific organization. For example, if your company produces a food product,
recalls could be an important topic to address. Be sure to apply course concepts, including those related to positive
messaging and crisis prevention/risk.
NOTE: Include the social media policy created during Unit VII as one section of the plan. You can update the policy
and make any necessary revisions to the version you submitted in Unit VII.

identify stakeholders who might be affected by the crisis,
Include procedures to communicate internally with those inside of the company and externally with stakeholders
outside of the company.

include clear, detailed procedures using a format that is easy to follow,
add any templates or worksheets that might be helpful for the leaders to use when responding to a crisis event, and
use text enhancements and visuals to emphasize and for clarity.

In addition to basic enhancements such as bold, underline, italics, caps, font/font size, and color-coding, you can
include graphs, illustrations, or other visual elements.

Your crisis communication plan must be at least 6 pages in length. Adhere to APA Style when creating citations and
references for this assignment. APA formatting, however, is not necessary.

Note: In Unit I, you developed a definition of an organizational crisis and you have been applying that definition to your written
work throughout the term. This definition should become the basis for your crisis communication plan. In Unit II, you were
introduced to several key crisis communication theories. Rely on these concepts to guide your plan. Both the definition you
created in Unit I and the theories you learned about in Unit II should provide justification for your specific strategy. The Unit
VIII readings (Chapter 12 of your textbook) elaborate on a key theory presented in the course: discourse of renewal theory.

The four opportunities presented in the chapter are important aspects to consider as you develop the plan:

1. organizational learning,
2. ethical communication,
3. prospective rather than retrospective vision, and
4. effective organizational rhetoric.

To complete the assignment, you must write an original plan. Ensure you do not plagiarize another plan by using content in
any example crisis communication plans.

Submitting Course Papers/Projects

Assignment tab in each unit. Do not e-mail your paper directly to your professor. By using the Assignment tab, your record
will automatically be updated to indicate you have submitted your papers/projects, and the assignment will be provided to
your professor for grading. Instructions for submitting your assignment can be found under the Assignment tab in each unit.

COM 5360, Crisis Communication and Leadership 5

APA Guidelines

Waldorf University requires that students use the APA style for papers and projects. Therefore, the APA rules for formatting,
quoting, paraphrasing, citing, and listing of sources are to be followed. Information about using APA style can be found in
APA Style Help in the Course Menu. This area provides links to Internet sites, tutorials, and guides that provide
comprehensive information on APA formatting, including examples and sample papers.

This course utilizes analytic grading rubrics as tools for your professor in assigning grades for all learning activities. Each
rubric serves as a guide that communicates the expectations of the learning activity and describes the criteria for each level
meet the requirements of that learning activity. It is imperative for you to familiarize yourself with these rubrics because
these are the primary tools your professor uses for assessing learning activities.

Rubric categories include (1) Discussion Board, (2) Assessment (Written Response), and (3) Assignment. However, it is
possible that not all of the listed rubric types will be used in a single course (e.g., some courses may not have
Assessments).

The Discussion Board rubric can be found within Unit I’s Discussion Board submission instructions.

The Assessment (Written Response) rubric can be found embedded in a link within the directions for each Unit
Assessment. However, these rubrics will only be used when written-response questions appear within the Assessment.

Each Assignment type (e.g., article critique, case study, research paper) will have its own rubric. The Assignment rubrics
are built into Blackboard, allowing students to review them prior to beginning the Assignment and again once the
Assignment has been scored. This rubric can be accessed via the Assignment link located within the unit where it is to be

Again, it is vitally important for you to become familiar with these rubrics because their application to your
Discussion Boards, Assessments, and Assignments is the method by which your instructor assigns all grades.

Communication Forums

These are non-graded discussion forums that allow you to communicate with your professor and other students.
Participation in these discussion forums is encouraged, but not required. You can access these forums with the buttons in
the Course Menu. Instructions for subscribing/unsubscribing to these forums are provided below.

Click here for instructions on how to subscribe/unsubscribe and post to the Communication Forums.

This communication forum provides you with an opportunity to ask your professor general or course content questions.
Questions may focus on Blackboard locations of online course components, textbook or course content elaboration,

Questions that are specific in nature, such as inquiries regarding assessment/assignment grades or personal
accommodation requests, are NOT to be posted on this forum. If you have questions, comments, or concerns of a non-
professor within 48 hours.

Before posting, please ensure that you have read all relevant course documentation, including the syllabus,
assessment/assignment instructions, faculty feedback, and other important information.

Student Break Room

This communication forum allows for casual conversation with your classmates. Communication on this forum should
always maintain a standard of appropriateness and respect for your fellow classmates. This forum should NOT be used to

COM 5360, Crisis Communication and Leadership 6

The following pages contain a printable Course Schedule to assist you through this course. By following this schedule, you
will be assured that you will complete the course within the time allotted.

Unit I Defining Crisis Communication [ Weight: 10% ]

Chapter 1: Defining Crisis Communication
Unit Resource (1 video): See Study Guide

Discuss: Unit I Discussion Board 2%

Submit: Unit I Assignment 8%

Unit II Crisis Communication Theory in Practice [ Weight: 10% ]

Chapter 2: Understanding Crisis Communication Theory and Practice
Chapter 4: Applying the Lessons to Produce Effective Crisis Communication, pp. 57-60
Unit Resource (1 article): See Study Guide

Discuss: Unit II Discussion Board 2%

Submit: Unit II Case Study 8%

Unit III Approaches to Crisis Communication [ Weight: 10% ]

Chapter 3: Lessons on Effective Crisis Communication
Chapter 4: Applying the Lessons to Produce Effective Crisis Communication
Unit Resource (1 article): See Study Guide

Discuss: Unit III Discussion Board 2%

Submit: Unit III Case Study 8%

Unit IV Ethical Demands of the Leader [ Weight: 10% ]

Chapter 11: Responding to the Ethical Demands of Crisis

Discuss: Unit IV Discussion Board 2%

Submit: Unit IV Assignment 8%

COM 5360, Crisis Communication and Leadership 7

Unit V Leading During Times of Uncertainty [ Weight: 10% ]

Chapter 5: Lessons on Managing Crisis Uncertainty Effectively
Chapter 6: Applying the Lessons for Managing Crisis Uncertainty Effectively
Unit Resources (1 article, 1 video): See Study Guide

Discuss: Unit V Discussion Board 2%

Submit: Unit V Assignment 8%

Unit VI Recovery and Renewal [ Weight: 10% ]

Chapter 7: Lessons on Effective Crisis Leadership
Chapter 8: Applying the Lessons for Developing Effective Crisis Leadership

Discuss: Unit VI Discussion Board 2%

Submit: Unit VI PowerPoint Presentation 8%

Unit VII Positive Messaging and Neutralizing Risk [ Weight: 10% ]

Chapter 9: Learning Through Failure
Chapter 10: Risk Communication

Discuss: Unit VII Discussion Board 2%

Submit: Unit VII Assignment 8%

Unit VIII Creating a Crisis Communication Plan [ Weight: 30% ]

Chapter 12: Facilitating Renewal Through Effective Crisis Communication

Discuss: Unit VIII Discussion Board 2%

Submit: Unit VIII Final Project 28%

COM 5360, Crisis Communication and Leadership 8

• COM 5360, Crisis Communication and Leadership
• Course Syllabus
• Course Description
• Course Textbook(s)
• Course Learning Outcomes
• Credits
• Course Structure
• Unit Assignments
• Unit I Assignment
• Unit II Case Study
• Unit III Case Study
• Unit IV Assignment
• Part I: Introduction and Outline
• Part II: Code of Ethics
• Unit V Assignment
• Press Release
• Unit VI PowerPoint Presentation
• PowerPoint Presentation
• Unit VII Assignment
• Social Media Policy
• Unit VIII Final Project
• Crisis Communication Plan
• Submitting Course Papers/Projects
• APA Guidelines
• Communication Forums

## 2

Analyze the Policy Analysis Process

A critical aspect of policy analysis is development. Employees are the most valuable asset within an organization. Policies serve as a framework to guide decision making.

Your assignment this week is to analyze the framework toward the creation of a policy and the process involved. Then, you will compare two similar policies from different organizations that address a current HRM issue and analyze if the policies are clearly defined. Examples can consist of but not include: computer usage at work (personal e-mail), cellphone use policy, attire and grooming policy, etc. This will serve as preparation toward revising a policy within your organization. Be sure to consider what you learned during this week’s resources and the additional scholarly resources you gathered to analyze the policy development process.

Prepare an infographic that answers the following questions:

· What steps are required in policy analysis?

· What collaboration is required to create policy?

· What factors contributed to creating policy?

· What controversy could emerge during the analysis process?

Length: May vary depending on the content

References:  Include a minimum of 3 scholarly sources. In addition, other appropriate scholarly resources may be included.

## 2

1

2

75%
SIMILARITY INDEX

66%
INTERNET SOURCES

34%
PUBLICATIONS

72%
STUDENT PAPERS

1 41%
2 34%

Exclude quotes Off

Exclude bibliography Off

Exclude matches Off

inf…pdf
ORIGINALITY REPORT

PRIMARY SOURCES

onlinelibrary.wiley.com
Internet Source

Christian Rosser, Sabrina A. Ilgenstein, Fritz
Sager. “The Iterative Process of Legitimacy-
Building in Hybrid Organizations”,
Publication

## #2

_____________________

Topography homework Name ___________________________
20 points total

1) Download the worksheet and keep a clean copy of the file on a safe place like your homework
file. You have created it on your computer desktop.

2) Most of you do not know how to read topographic maps, if you do go ahead and get it done.
But if you do not know, then read the information in the two links. You do not need to buy the
book!

3) Print a copy of the worksheet and get a light brown or green coloring pencil. Locate the 0
elevation contour line and color all the area above sea level this is elevation greater than 0.
Positive values indicate above sea level, negative values below sea level. So now you can see the
island of Puerto Rico and the Puerto Rico Trough or Trench as well as the Hawaiian Islands.
These depth values are in meters.

4) Find the highest positive values Max elevation and Max depth highest negative values found
across the straight lines (vertical cross sections) across the contour lines. This thick straight line is
the line of the vertical section or profile. These sections depict the variation in elevation along the
line. The panels: A, B, C and D are their graphic representations.

5) To select which cross section is the right one look for the starting height or water depth at the
beginning and end of the lines. Then look in between too!

Questions:

1. Answer the following questions regarding Figure (1) below:
a. What is the maximum depth you would reach if you traversed along the

path shown below (2 pts)? ___________________
b. What is the maximum height you would reach if you traveled along the

same path (2 pts)? ___________________
c. Between what 2 depths would you experience the greatest slope (2 pts)?

d. Choose which subpanel in Figure (2) best represents the cross-section
shown below (6 pts). __________________

1

.5

17
-68 -65

18

Figure 1 (contour lines are in meters)

2

000
A

4000
B

2000 2000

E 0 0 -£ -2000
a.

-2000

~ -4000 -4000

-6000 -6000

-8000 -8000

4000
C

4000
D

2000 2000

– o, ~ 0 E -£ -2000
a.

-2000

~ -4000 -4000

-6000 -6000

-8000 -8000

4

Figure 2

2. Answer the following questions regarding Figure(3) on the next page:
a. What is the maximum depth you would reach if you traversed along the

path shown in Figure (3) (3 pts)? ___________________
b. What is the maximum height you would reach if you traveled along the

same path (3 pts)? ___________________
c. Choose which subpanel in Figure (4) best represents the cross-section

shown on Figure(3) (4 pts). __________________

3

~Cl 24 .I>

0 ••• •••• :2 –~~.
-g 21 -·.;::;
m

20

19

Q ..,

Figure 3 (contour lines are in meters)

4

4000
A B

2000 2000

– 0 0 E -£ -2000
a.

-2000
<ll
u -4000 -4000

-6000 -6000

-8000 -8000

4000 4000
C D

2000 2000

– 0 0 E -£ -2000
a.

-2000
<ll
u -4000 -4000

-6000 -6000

-8000 -8000

Figure 4

5

1. Name:
2. path shown below 2 pts:
3. same path 2 pts:
4. d Choose which subpanel in Figure 2 best represents the crosssection:
5. shown below 6 pts:
6. path shown in Figure 3 3 pts:
7. same path 3 pts:
8. shown on Figure3 4 pts:

## 2

Analyze the Policy Analysis Process

A critical aspect of policy analysis is development. Employees are the most valuable asset within an organization. Policies serve as a framework to guide decision making.

Your assignment this week is to analyze the framework toward the creation of a policy and the process involved. Then, you will compare two similar policies from different organizations that address a current HRM issue and analyze if the policies are clearly defined. Examples can consist of but not include: computer usage at work (personal e-mail), cellphone use policy, attire and grooming policy, etc. This will serve as preparation toward revising a policy within your organization. Be sure to consider what you learned during this week’s resources and the additional scholarly resources you gathered to analyze the policy development process.

Prepare an infographic that answers the following questions:

· What steps are required in policy analysis?

· What collaboration is required to create policy?

· What factors contributed to creating policy?

· What controversy could emerge during the analysis process?

Length: May vary depending on the content

References:  Include a minimum of 3 scholarly sources. In addition, other appropriate scholarly resources may be included.

## #2

Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Refer to the Discussion Forum Grading Rubric under the Settings icon above for guidance on how your discussion will be evaluated.

Making a Difference

Imagine you are a policymaker for your city or town. Based on what you know and what you have learned in this course, what would you modify or improve to make a positive change in the life of a vulnerable group we have not covered in class? Justify whether or not you would consult the vulnerable group when developing programs or policies? Propose a policy you would create to improve health care services accessibility, cost, and quality related to your selected group?

Your initial contribution should be 250 to 300 words in length. Your research and claims must be supported by your course text and at least one other scholarly source. Use proper APA formatting for in-text citations and references as outlined in the Writing Center.

## 2

392

12-1 Summarize the conclusions of trait

12-2 Identify the central tenets and main
limitations of behavioral theories.

12-3 Contrast contingency theories of

12-4 Describe the contemporary theories
to foundational theories.

12-5 Discuss the roles of leaders in
creating ethical organizations.

12-6 Describe how leaders can have a
positive impact on their organiza-
tions through building trust and
mentoring.

12-7 Identify the challenges to our

LEARNING OBJECTIV ES
After studying this chapter, you should be able to:

S
ou

rc
e:

M
ik

e
H

ut
ch

in
gs

/R
eu

te
rs

/A
la

m
y

S
to

ck
P

ho
to

M12_ROBB9329_18_SE_C12.indd 392 29/09/17 4:03 pm

Myth or
Science?

Career
OBjectives

An Ethical
Choice

Point/
Counterpoint

Experiential
Exercise

Ethical
Dilemma

Case
Incident 1

Case
Incident 2

Critical
Thinking ! ! ! ! ! ! !

Communication ! ! ! !
Collaboration ! ! ! !
Knowledge

Application and
Analysis

! ! ! ! ! ! ! !

Social
Responsibility ! ! !

Employability Skills Matrix (ESM)

MyLab Management Chapter Warm Up
If your professor has assigned this activity, go to www.pearson.com/mylab/management to complete the
chapter warm up.

FROM WACKY VISION TO TOTAL HOTEL INDUSTRY
DISRUPTION

In 2008, Brian Chesky and Joe Gebbia, design school graduates in Silicon Valley, had a wacky idea. Gebbia’s roommates suddenly moved out, and
he needed people to fill the remaining rooms. The idea to host a home-
sharing platform came to him and Chesky after Gebbia asked Chesky to
take the remaining room. The result was Air Bed & Breakfast (Airbnb). From
these humble (and sometimes rocky) beginnings, Airbnb bourgeoned to
a \$31 billion organization, nearly the same valuation as Marriott Interna-
tional, without owning a single room. To date, the company has housed
over 150 million guests in over 65,000 cities in over 191 countries. It also
has more than 3 million listings worldwide (including over 1,400 castles).

Part of the reason for the major success of Airbnb is its executive leader-
ship and top management team. Chesky, as CEO (shown here meeting with
an Airbnb host in South Africa), has guided the organization through remark-
ably turbulent times throughout its development, with no prior business
experience. In 2017, Chesky has been listed as one of the World’s Greatest
Leaders by Fortune. The caring leadership style of Chesky offers a counter-
point to that exhibited by leadership in other sharing-economy brands, such
as Uber, who have come under fire for an apparent aggressive and sexist
culture and whose CEO, Travis Kalanick, was caught on video verbally berat-
ing an Uber driver.

M12_ROBB9329_18_SE_C12.indd 393 29/09/17 4:03 pm

394 PART 3 The Group

Perhaps what drives the success of Chesky is the charisma, authentic-
ity, and ethicality with which he meets leadership challenges. His mentor,
Warren Buffett (CEO of Berkshire Hathaway), notes that Brian “feels it all
the way through. I think he would be doing what he’s doing if he didn’t get
paid a dime for it.” A trait that Chesky believes is important for handling
leadership challenges is humility. Chesky realizes that it is easy for lead-
ers to become defensive when they are challenged, but sometimes leaders
must take a step back and approach their challenges with humility and
acceptance.

ers, “we need to have mentors. I think I’ve always been pretty shameless
about seeking out people much smarter and much more experienced than
me from the very beginning … and the more successful I got, the more lead-
ers I started seeking out, whether it was investors, or Sheryl Sandberg at
Facebook, or … Warren Buffett.” Perhaps the ethicality with which Chesky
approaches Airbnb is reflected in the company’s new vision statement:
“Belong Anywhere.” New leaders within the organization, such as Beth Axel-
rod, the new vice president of employee experience, are modeling this mis-
sion and enacting it “to create belonging everywhere” through recruitment,
selection, employee engagement, and motivation at Airbnb.

April 12, 2017; L. Gallagher, “Airbnb’s IPO Runway,” Fortune, March 17, 2017, http://
fortune.com/2017/03/17/airbnbs-ipo-runway/; L. Gallagher, “Q&A with Brian Chesky:
Disruption, Leadership, and Airbnb’s Future,” Fortune, March 27, 2017, http://fortune
.com/2017/03/27/chesky-airbnb-leadership-uber/; L. Gallagher, The Airbnb Story: How
Three Ordinary Guys Disrupted an Industry, Made Billions … and Created Plenty of Con-
troversy (New York, NY: Houghton Mifflin Harcourt, 2017); L. Gallagher, “Why Airbnb CEO
Brian Chesky Is Among the World’s Greatest Leaders,” Fortune, March 24, 2017, http://
“Exclusive: Meet the Woman Joining Airbnb’s Executive Team,” Fortune, January 13, 2017,
http://fortune.com/2017/01/13/airbnb-executive-beth-axelrod/.

Leaders like Brian Chesky possess a special something that sets them apart. However, theirs is not the only type of effective leadership. In this chapter,
ers. First, we’ll present trait theories of leadership. Then, we’ll discuss chal-
lenges to the meaning and importance of leadership. But before we begin, let’s
clarify what we mean by the term leadership.

We define leadership as the ability to influence a group toward the achieve-
ment of a vision or set of goals. But not all leaders are managers, nor are all
managers leaders. Just because an organization provides its managers with cer-
tain formal rights does not mean that they will lead effectively. Leaders can
emerge from within a group as well as by formal appointment. Nonsanctioned
leadership—the ability to influence that arises outside the formal structure
of the organization—is often as important, or more important, than formal
influence.

leadership The ability to influence a group
toward the achievement of a vision or set of
goals.

M12_ROBB9329_18_SE_C12.indd 394 29/09/17 4:03 pm

Organizations need strong leadership and strong management for optimal
effectiveness. We need leaders to challenge the status quo, create visions of the
future, and inspire organizational members to achieve the visions. We need
managers to formulate detailed plans, create efficient organizational struc-
tures, and oversee day-to-day operations.

Trait Theories
Throughout history, strong leaders have been described by their traits. There-
fore, leadership research has long sought to identify the personality, social,
Trait theories of leadership focus on personal qualities and characteristics.1

For personality, comprehensive reviews of the leadership literature orga-
nized around the Big Five framework have found extraversion to be the most
predictive trait of effective leadership.2 However, extraversion is perhaps more
related to the way leaders emerge than it is related to their effectiveness. Socia-
ble and dominant people are more likely to assert themselves in group situ-
ations, which can help extraverts be identified as leaders. However, effective
leaders do not tend to be domineering. One study found that leaders who
scored very high in assertiveness, a facet of extraversion, were less effective than
those who were moderately high.3 Extraverted leaders may be more effective
when leading groups of passive employees rather than proactive employees.4
Although extraversion can predict effective leadership, the relationship may be
due to unique facets of the trait and the situation.

Unlike agreeableness and emotional stability, which do not seem to predict
ership, especially leader effectiveness. For example, multi-source data (i.e.,
from employees, coworkers, and supervisors) from a Fortune 500 organiza-
tion suggest that conscientiousness facets, such as achievement striving and
dutifulness, are related to leader emergence.5 Also, achievement striving
and dependability were found to be related to effectiveness as a manager.6 In
sum, leaders who like being around people, who can assert themselves (extra-
verted), and who are disciplined and able to keep commitments they make

What about the Dark Side personality traits of Machiavellianism, narcis-
sism, and psychopathy (see Chapter 5)? Research indicates they’re not all bad
for leadership. A study in Europe and the United States found that normative
(midrange) scores on the Dark Side personality traits were optimal, while low
(and high) scores were associated with ineffective leadership. The study sug-
gested that high emotional stability may accentuate the ineffective behaviors.7
However, higher scores on Dark Side traits and emotional stability can contrib-
ute to leadership emergence. Thankfully, both this study and other interna-
tional research indicate that building self-awareness and self-regulation skills
may be helpful for leaders to control the effects of their Dark Side traits.8

Another trait that may indicate effective leadership is emotional intelligence
(EI), discussed in Chapter 4. A core component of EI is empathy. Empathetic

12-1 Summarize the conclu-sions of trait theories

trait theories of leadership Theories that
consider personal qualities and characteris-

MyLab Management Watch It
If your professor has assigned this activity, go to www.pearson.com/
mylab/management to complete the video exercise.

M12_ROBB9329_18_SE_C12.indd 395 29/09/17 4:03 pm

396 PART 3 The Group

leaders can sense others’ needs, listen to what followers say (and don’t say),
and read the reactions of others. A leader who displays and manages emotions
effectively will find it easier to influence the feelings of followers by express-
ing genuine sympathy and enthusiasm for good performance, and by showing
irritation when employees fail to perform.9 Although the association between
in this chapter) was moderate, it is much weaker when followers rate their lead-
ers’ leadership behaviors.10 However, research has demonstrated that people
high in EI are more likely to emerge as leaders, even after taking cognitive abil-
ity and personality into account.11

Based on the latest findings, we offer two conclusions. First, we can say that
traits can predict leadership. Second, traits do a better job predicting the emer-
The fact that an individual exhibits the right traits and others consider that per-
son a leader does not necessarily mean he or she will be an effective one.

Trait theories help us predict leadership, but they don’t fully explain leader-
ship. What do successful leaders do that makes them effective? Are different
types of leader behaviors equally effective? Behavioral theories, discussed next,
help us define the parameters of leadership.

Behavioral Theories
Trait research provides a basis for selecting the right people for leadership.
Behavioral theories of leadership, in contrast, imply we can train people to be

The most comprehensive behavioral theories of leadership resulted from
the Ohio State Studies,13 which sought to identify independent dimensions of
leader behavior. Beginning with more than a thousand dimensions, the studies
narrowed the list to two that substantially accounted for most of the leadership
behavior described by employees: initiating structure and consideration.

Initiating structure is the extent to which a leader defines and structures
his or her role and those of the subordinates to facilitate goal attainment.

12-2 Identify the central tenets and main limitations of
behavioral theories.

proposing that specific behaviors differentiate

initiating structure The extent to which a
leader defines and structures his or her role
and those of the subordinates to facilitate
goal attainment.

As the CEO of Women’s Bean Project,
Tamra Ryan leads a team of pro-
fessionals in managing the social
enterprise that helps women earn a
living while teaching them work and
life skills. Her traits of extraversion,
conscientiousness, confidence, and
emotional stability contribute to her
success.
Source: David Zalubowski/AP Images

M12_ROBB9329_18_SE_C12.indd 396 29/09/17 4:03 pm

It includes behavior that attempts to organize work, work relationships, and
goals. A leader high in initiating structure is someone who assigns follow-
ers particular tasks, sets definite standards of performance, and emphasizes

Consideration is the extent to which a leader has job relationships that are
characterized by mutual trust, respect for employees’ ideas, and regard for
their feelings. A leader high in consideration helps employees with personal
problems, is friendly and approachable, treats all employees as equals, and
expresses appreciation and support (people-oriented). Most of us want to work
work, 66 percent of U.S. employees surveyed mentioned appreciation.14

The results of behavioral theory studies have been fairly positive. For exam-
ple, one review found the followers of leaders high in consideration (and, to
a lesser degree, initiating structure) were more satisfied with their jobs, were
and initiating structure were found to be moderately related to leader and
group performance along with ratings of leader effectiveness.15 However,

consideration The extent to which a leader
has job relationships that are characterized by
mutual trust, respect for subordinates’ ideas,
and regard for their feelings.

Career OBjectives
How can I get my boss to be a better leader?

My boss is the CEO, and she’s a gos-
team personal questions and sharing
information with anyone. The other
day, I caught her e-mailing my col-
league about my salary and career
prospects! What should I do about her

— Phil
Dear Phil,
Nobody likes an oversharer! Perhaps
your boss isn’t aware of the impact
of her behavior and thinks she is just
being friendly. Assuming this is the
case, you might be able to make her
think first before sharing. If you’re
suggest a private meeting to discuss
your concerns. You should bring a list
of the types of information she solic-
its and shares—with an example or
two—and, if she’s open to discus-
sion, problem-solve with her about her
habit. She may see that her open-book
ship effectiveness.

Another tactic might be starting with
researching the best privacy practices,
laws, and business guidelines. Be sure

resources handbook for any men-
tions of privacy expectations. Then, in
your meeting, you could present your
research findings.

With both direct approaches, you run
the risk of offending your boss, which
may very well happen if she becomes
embarrassed. And she may defend her
behavior and not see the problem if her
oversharing is actually strategic gossip,
which could have ramifications for what
she then thinks and says about you!

These approaches still might be
worth trying, but from what you’ve said
about her, it’s highly unlikely she will
change her general behavior. Research
indicates that her personal tendencies
will prevail over time. It sounds like she
is extraverted, for instance, and you’re
not going to change that. She may be
clever and manipulative, purposefully
leveraging her information for personal
gain without a concern for others (high-
Machiavellian or narcissistic). In that
case self-awareness can help, but her
behavior won’t change unless she is
willing to practice self-regulation.

Perhaps most important, it doesn’t
seem that you like your boss. This may

be a real problem that you cannot sur-
mount. How are you going to build a
relationship of trust with her, trust that
will be needed for you to continue to
feel motivated and work hard? Unfortu-
nately, if you cannot thrive in this envi-
ronment, it may be best to move on.

Good luck for your best possible
outcome!

Sources: Based on A. E. Colbert, M. R.
Barrick, and B. H. Bradley, “Personality
and Leadership Composition in Top Man-
agement Teams: Implications for Organiza-
tional Effectiveness,” Personnel Psychology
67 (2014): 351–87; R. B. Kaiser, J. M.
LeBreton, and J. Hogan, “The Dark Side of
Applied Psychology: An International Review
64, no. 1 (2015): 55–92; and R. Walker,
“A! Boss Who Shares Too Much,” The New
York Times, December 28, 2014, 7.

The opinions provided here are of the man-
agers and authors only and do not neces-
sarily reflect those of their organizations.
The authors or managers are not respon-
sible for any errors or omissions, or for the
results obtained from the use of this!infor-
mation. In no event will the authors or
managers, or their related partnerships
or corporations thereof, be liable to you
or anyone else for any decision made or
action taken in reliance on the opinions
provided here.

M12_ROBB9329_18_SE_C12.indd 397 29/09/17 4:03 pm

398 PART 3 The Group

results of behavioral theory tests may vary across cultures. Research from the
GLOBE program—a study of 18,000 leaders from 825 organizations in 62
countries that was discussed in Chapter 5—suggested there are international
differences in the preference for initiating structure and consideration.16 The
study found that leaders high in consideration succeeded best in countries
where cultural values did not favor unilateral decision making, such as Brazil.
In contrast, the French have a more bureaucratic view of leaders and are less
likely to expect them to be humane and considerate. A leader high in initiating
structure (relatively task-oriented) will do best there and can make decisions
in a relatively autocratic manner. In other cultures, both dimensions may be
important—Chinese culture emphasizes being polite, considerate, and unself-
ish, but it has a high-performance orientation. Thus, consideration and initiat-
ing structure may both be important for a manager to be effective in China.

Summary of Trait Theories and Behavioral Theories
In general, research indicates there is validity for both the trait and behavioral
theories. Parts of each theory can help explain facets of leadership emergence
and effectiveness. However, identifying the exact relationships is not a simple
task. The first difficulty is in correctly identifying whether a trait or a behavior
predicts a certain outcome. The second is in exploring which combinations
of traits and behaviors yield certain outcomes. The third challenge is to deter-
mine the causality of traits to behaviors so that predictions toward desirable

As important as traits and behaviors are in identifying effective or ineffec-
tive leaders, they do not guarantee success. Some leaders may have the right
traits or display the right behaviors and still fail. Context matters too, which has
given rise to the contingency theories we discuss next.

Contingency Theories
Some leaders seem to gain a lot of admirers when they take over struggling
is more complex than finding a few “heroes” to help lift the organization out of
the mire. Also, the leadership style that works in tough times doesn’t necessarily
translate to long-term success. According to Fred Fiedler, it appears that under
condition a, leadership style x would be appropriate, whereas style y would be
more suitable for condition b, and style z for condition c. But what were condi-
tions a, b, and c? We next consider the Fiedler model, one approach to isolating
situational variables.

The Fiedler Model
Fred Fiedler developed the first comprehensive contingency model for lead-
ership.17 The Fiedler contingency model proposes that group performance
depends on the proper match between the leader’s style and the degree to
which the situation gives the leader control. According to this model, the indi-
vidual’s leadership style is assumed to be stable or permanent. The least pre-
ferred coworker (LPC) questionnaire identifies whether a person is task-oriented
or relationship-oriented by asking respondents to think of all the coworkers they
have ever had and describe the one they least enjoyed working with.18 If you
describe this person in favorable terms (a high LPC score), you are relationship-
oriented. If you see your least-preferred coworker in unfavorable terms (a low
LPC score), you are primarily interested in productivity and are task-oriented.

12-3 Contrast contingency theories of leadership.

Fiedler contingency model The theory that
effective groups depend on a proper match
between a leader’s style of interacting with
subordinates and the degree to which the
situation gives control and influence to the

least preferred coworker (LPC)
questionnaire An instrument that purports
to measure whether a person is task- or
relationship-oriented.

M12_ROBB9329_18_SE_C12.indd 398 29/09/17 4:03 pm

After finding a score, a fit must be found between the organizational situa-
tion and the leader’s style for there to be leadership effectiveness. We can assess
the situation in terms of three contingency or situational dimensions:

1. Leader–member relations is the degree of confidence, trust, and respect
that members have in their leader.

2. Task structure is the degree to which the job assignments are regimented
(that is, structured or unstructured).

3. Position power is the degree of influence a leader has over power variables
such as hiring, firing, discipline, promotions, and salary increases.

According to the model, the higher the task structure, the more procedures
are added, and the stronger the position power, the more control the leader
has. A very favorable situation (in which the leader has a great deal of control)
might include a payroll manager who has the respect and confidence of his or
her employees (good leader–member relations); activities that are clear and
specific—such as wage computation, check writing, and report filing (high task
structure); and considerable freedom to reward and punish employees (strong
position power). The favorable situations are on the left side of the model in
Exhibit 12-1. An unfavorable situation, to the right in the exhibit, might be
that of the disliked chairperson of a volunteer United Way fundraising team
job, the leader has very little control. When faced with a category I, II, III, VII,
leaders (represented by the solid line), however, perform better in moderately
favorable situations—categories IV, V, and VI.

Studies testing the overall validity of the Fiedler model were initially sup-
portive, but the model hasn’t been studied much in recent years.19 While it
provides some insights that we should consider, its strict practical application is
problematic.

of confidence, trust, and respect that

task structure The degree to which job
assignments are regimented.

position power Influence derived from one’s
formal structural position in the organization;
includes the power to hire, fire, discipline,
promote, and give salary increases.

Findings from the Fiedler ModelExhibit 12-1

Good

High

Strong

Good

High

Weak

Good

Low

Strong

Good

Relationship oriented

Good

Poor

Category

Position power

Favorable Moderate Unfavorable

Pe
rf

or
m

an
ce

Low

Weak

Poor

High

Strong

Poor

High

Weak

Poor

Low

Strong

Poor

Low

Weak

I II III IV V VI VII VIII

M12_ROBB9329_18_SE_C12.indd 399 29/09/17 4:03 pm

400 PART 3 The Group

Situational leadership theory (SLT) focuses on the followers. It says that suc-
on the followers’ readiness, the extent to which followers are willing and able
to accomplish a specific task. A leader should choose one of four behaviors

If followers are unable and unwilling to do a task, the leader needs to give
clear and specific directions; if they are unable but willing, the leader needs to
display a high task orientation to compensate for followers’ lack of ability, and
high relationship orientation to get them to accept the leader’s desires. If fol-
lowers are able but unwilling, the leader needs to use a supportive and participa-
tive style; if they are both able and willing, the leader doesn’t need to do much.

SLT has intuitive appeal. It acknowledges the importance of followers and
builds on the logic that leaders can compensate for followers’ limited ability
and motivation. Yet research efforts to test and support the theory have gener-
ally been disappointing.21 Why? Possible explanations include internal ambi-
guities and inconsistencies in the model itself, as well as problems with research
methodology. Despite its intuitive appeal and wide popularity, any endorse-
ment must be cautious for now.

Path–Goal Theory
Developed by Robert House, path–goal theory extracts elements from the
research on initiating structure and consideration, and on the expectancy
theory of motivation.22 Path–goal theory suggests that it’s the leader’s job to
provide followers with information, support, or other resources necessary to
achieve goals. (The term path–goal implies effective leaders clarify followers’
paths to their work goals and make the journey easier by reducing roadblocks.)
The theory predicts the following:

or stressful than when they are highly structured and well laid out.

• Supportive leadership results in high employee performance and satisfaction when

• Directive leadership is likely to be perceived as redundant among employees with
high ability or considerable experience.

Like SLT, path–goal theory has intuitive appeal, especially from a goal
attainment perspective. Also like SLT, the theory can be adopted only cau-
tiously for application, but it is a useful framework in examining the vital role

The final contingency theory we cover argues that the way the leader makes
decisions is as important as what he or she decides. The leader–participation
model relates leadership behavior to subordinate participation in decision
making.24 Like path–goal theory, it says that leader behavior must adjust to
reflect the task structure (such as routine, nonroutine, or in between), but it
does not cover all leadership behaviors and is limited to recommending what
types of decisions might be best made with subordinate participation. It lays
the groundwork for the situations and leadership behaviors most likely to elicit
acceptance from subordinates.

ership is a symbiotic relationship between leaders and followers.25 But the theo-
ries we’ve covered to this point assume that leaders use a homogeneous style

A contingency theory that focuses on

path–goal theory A theory stating that it
is the leader’s job to assist followers in
attaining their goals and to provide the
necessary direction and/or support to ensure
that their goals are compatible with the overall
objectives of the group or organization.

theory that provides a set of rules to
determine the form and amount of
participative decision making in different
situations.

M12_ROBB9329_18_SE_C12.indd 400 29/09/17 4:03 pm

with everyone in their work unit. Think about your experiences in groups. Did
leaders often act very differently toward different people? Before we dig into

Leaders are important—to organizations, and to employees. The understand-
ing of leadership is a constantly evolving science. Contemporary theories have
been built on the foundation we’ve just established to discover unique ways
leaders emerge, influence, and guide their employees and organizations. Let’s
explore some of the current leading concepts, and look for aspects of the theo-

Think of a leader you know. Does this leader have favorites who make up an
theory.26 Leader–member exchange (LMX) theory argues that, because of time
pressures, leaders establish a special relationship with a small group of their
followers. These individuals make up the ingroup—they are trusted, get a dis-
proportionate amount of the leader’s attention, and are more likely to receive
special privileges. Other followers fall into the outgroup.

LMX theory proposes that early in the history of the interaction between a
leader and a given follower, the leader implicitly categorizes the follower as an
“in” or an “out”; that relationship becomes relatively stable over time. Leaders
induce LMX by rewarding employees with whom they want a closer linkage and
punishing those with whom they do not.27 For the LMX relationship to remain
intact, the leader and the follower must invest in the relationship.

Just how the leader chooses who falls into each category is unclear, but
there is evidence that ingroup members have demographic, attitude, and per-
sonality characteristics that are similar to those of their leader or a higher level

12-4 Describe the con-temporary theories of