Operations Management: Processes and Supply Chains, 12e (Krajewski)
Supplement E Simulation
1) Simulation is the process of reproducing the behavior of a system using a model that describes the
processes of the system.
2) Time compression is the feature of simulation that allows managers to obtain operating-characteristic
estimates in much less time than is required to gather the same operating data from a real system.
3) A simulation model:
A) describes operating characteristics with known equations.
B) replicates the service of customers and keeps track of characteristics such as the number in line, the
waiting time, and the total time in the system.
C) prescribes what should be done in a situation.
D) finds the optimal solution to a problem without having to try each alternative.
4) Simulation models are:
A) useful when waiting line models are too complex.
B) useful for conducting experiments using the real system.
C) preferred because they find optimal solutions.
D) usually inexpensive relative to other approaches.
5) Using a simulation model to gather a year of operating data in a few minutes is known as:
A) historical search data collection.
B) Monte Carlo optimization.
C) sub-optimization.
D) time compression.
6) ________ is the act of reproducing the behavior of a system using a model that describes the processes
of the system.
7) ________ is a feature of simulation models that allows them to obtain operating-characteristic estimates
in much less time than is required to gather the same operating data from a real system.
8) What is the difference between a waiting line model as described in Supplement B and a simulation
model of a waiting line problem?
9) What is meant by time compression in a simulation model?
10) What are the motivations for using simulation for analyzing processes?
11) What are the differences between decision variables and uncontrolled variables? Describe the
differences and provide an example from a simulation model.
Answer: A decision variable is one that is under control of the decision maker and will change from one
E.2 The Monte Carlo Simulation Process
1) Monte Carlo simulation is the use of computer graphics to show customers or products moving
through a series of process steps.
2) Any random number has the same likelihood of being selected as any other, regardless of how recently
it has been selected.
3) Random variables are under the control of the decision maker.
4) A manager has been given the table shown below and is asked to generate random numbers. Which of
the following statements is true?
Range
# Customers
00-49
0
50-79
1
80-99
2
A) There are no customers in the store 49 percent of the time.
B) The probability of having one customer in the store is 0.30.
C) The relative frequency of having two customers in the store is 0.80.
D) If we randomly choose the numbers 0 through 99 enough times, about 99 percent of the time we will
have two customers in the store.
5) Which one of the following relationships is correct?
A) Decision variables reflect the value of uncontrollable variables.
B) Dependent variables reflect the value of decision and uncontrollable variables.
C) Uncontrollable variables reflect the value of decision variables.
D) Uncontrollable variables reflect the values of dependent variables.
6) The manager of a branch bank wants to build a simulation model of the lobby operation to reduce the
waiting time of her customers. The number of tellers is an example of:
A) a decision variable.
B) an uncontrollable variable.
C) a time-compressed variable.
D) a dependent variable.
7) The manager of a branch bank wants to build a simulation model of the lobby operation to reduce the
waiting time of her customers. The number of customers arriving at any point of time is an example of
a(n):
A) decision variable.
B) uncontrollable variable.
C) time-compressed variable.
D) dependent variable.
8) The manager of a branch bank wants to build a simulation model of the lobby operation to reduce the
waiting time of her customers. The number of customers waiting in line at any point of time is an
example of a(n):
A) decision variable.
B) dependent variable.
C) uncontrollable variable.
D) time-compressed variable.
9) Which one of the following statements regarding simulation analysis is false?
A) Simulation analysis is a form of hypothesis testing.
B) In simulation, dependent variables reflect the values of both the decision variables and the
uncontrollable variables.
C) Statistical methods require the replication of simulation runs.
D) Each time a simulation model is run for a given set of decision variables, the same random numbers
must be used.
10) To generate 100 random numbers in an Excel simulation, the “=RAND()” function is first typed into
spreadsheet to cover the cells:
A) A1:E5.
B) A1:H12.
C) A1:J10.
D) A1:E22.
11) To generate 80 random numbers in an Excel simulation, the “=RAND()” function is first typed into the
cover the cells:
A) C2:G13.
B) C2:J11.
C) C2:F20.
D) C2:D40.
12) When using Excel for simulation, it is important to freeze the random numbers used in order to
compare the effectiveness of different policies. To do this, you must select the cells holding the random
numbers with the mouse, click Edit/Copy at the top of the spreadsheet, and:
A) click Edit/Paste Special and select the Values option.
B) click Edit/Paste to freeze the cells.
C) click Edit/Paste Special and select the Formulas option.
D) move to a different section of the spreadsheet, then click Edit/Paste to freeze the cells.
13) This table shows the distribution of grades in an operations management class.
Probability
Grade
.32
F
.20
D
.25
C
.18
B
.05
A
Add a column to the table that shows the cumulative probability and indicate what letter grade is
obtained when the RAND() function is equal to 0.5548.
A) A
B) B
C) C
D) D
14) This table shows the distribution of grades in an operations management class.
Probability
Grade
.32
F
.20
D
.25
C
.18
B
.05
A
Add a column to the table that shows the cumulative probability and indicate what letter grade is
obtained when the RAND() function is equal to 0.982245.
A) A
B) B
C) C
D) F
15) This table shows the distribution of grades in an operations management class.
Probability
Grade
Lower Range
.32
F
0
.20
D
0.32
.25
C
0.52
.18
B
0.77
.05
A
0.82
Add a column to the table that shows the cumulative probability and indicate what letter grade is
obtained when the RAND() function is equal to 0.7406.
A) A
B) B
C) C
D) D
16) ________ uses random numbers to generate simulation events.
17) If the data needed to set up a simulation are available in company records, the technique used to
obtain them is called ________.
18) A number that has the same probability of being selected as any other number is a(n) ________.
19) A variable that is controlled by the decision-maker and will change from one run to the next as
different events are simulated is a(n) ________.
20) ________ are random events that the decision maker cannot control.
21) If the difference in results between different simulation runs results in a mathematical difference in
system performance, the difference is said to be ________.
22) Why would data need to be collected prior to conducting a simulation?
23) How can random numbers be generated?
Answer: Random numbers can be generated by a computer, looking them up in a collection, or
generation by some mechanical means. A package like Excel can generate random numbers using the
E.3 Simulation with Excel Spreadsheets
1) In Excel, the RAND() function generates either a 0 or a 1, purely at random.
2) Steady state occurs when the simulation is repeated over enough time that the average results for
performance measures remain constant.
3) A simulation model is used to test the impact of the number of sample customers at a supermarket. As
the model is run, the decision maker watches the average number of customers in the store rapidly
increase from zero until it levels off and holds a constant value. The simulation model is:
A) not valid due to the lack of change.
B) in steady state.
C) not valid due to the fluctuation in the statistics.
D) a random variable.
4) One hundred monkeys are typing in Excel spreadsheets when one of them enters
=NORM.S.INV(RAND()) What is the result of this monkey’s function?
A) the number zero
B) random numbers evenly distributed from 0 to 1 inclusive
C) probabilities of the normal distribution function
D) z-scores from the standard normal distribution
5) In Excel, typing the function ________ will generate random numbers within the interval 0 to 1.
6) ________ occurs when the simulation is repeated over enough time that the average results for
performance measures remain constant.
7) What is steady state in a simulation model? Why is it important to achieve steady state?
Answer: Steady state occurs when the model under testing has moved past the transient state and
8) Describe a general procedure for generating normally distributed random numbers with a mean of 450
and standard deviation of 50 using Excel functions.