Krajewski Om9 Tif 04 SuppB
Krajewski Om9 Tif 04 SuppB
Krajewski Om9 Tif 04 SuppB
Supplement
B Simulation Models
TRUE/FALSE
1. Simulation is the process of reproducing the behavior of a system using a model that
describes the processes of the system.
Answer: True
Reference: Reasons for Using Simulation
Difficulty: Easy
Keywords: simulation, system behavior, model
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.
Answer: True
Reference: Reasons for Using Simulation
Difficulty: Moderate
Keywords: time compression
4. Decision variables are random events that the decision maker cannot control.
Answer: False
Reference: The Simulation Process
Difficulty: Moderate
Keywords: decision variable
5. A statistically significant difference in simulation results, when acted upon by the manager,
will result in significant process improvements in the eyes of the customer or company or
both.
Answer: False
Reference: The Simulation Process
Difficulty: Moderate
Keywords: managerial decisions, statistically significant results
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6. Steady state occurs when the simulation is repeated over enough time that the average results
for performance measures remain constant.
Answer: True
Reference: Computer Simulation
Difficulty: Moderate
Keywords: steady state, simulation repetition
MULTIPLE CHOICE
7. 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.
Answer: b
Reference: Reasons for Using Simulation
Difficulty: Easy
Keywords: simulation model
9. 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
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10. 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. suboptimization.
d. time compression.
Answer: d
Reference: Reasons for Using Simulation
Difficulty: Moderate
Keywords: time compression
12. A number that has the same probability of being selected as any other is called a(n):
a. Monte Carlo number.
b. decision number.
c. uncontrolled number.
d. random number.
Answer: d
Reference: The Simulation Process
Difficulty: Moderate
Keywords: random number
13. 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.
Answer: a
Reference: The Simulation Process
Difficulty: Moderate
Keywords: decision variable
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14. 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. a decision variable.
b. an uncontrollable variable.
c. a time-compressed variable.
d. a dependent variable.
Answer: b
Reference: The Simulation Process
Difficulty: Moderate
Keywords: uncontrollable variable
15. 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. a decision variable.
b. a dependent variable.
c. an uncontrollable variable.
d. a time-compressed variable.
Answer: b
Reference: The Simulation Process
Difficulty: Moderate
Keywords: dependent variable
16. 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.
Answer: d
Reference: The Simulation Process
Difficulty: Hard
Keywords: random number
17. To generate 100 random numbers in an Excel simulation, the “=RAND()” function is first
typed into the A1 cell on an Excel spreadsheet. A1 can then be copied and pasted in a
rectangular area on the spreadsheet to cover the cells:
a. A1:E5
b. A1:H12
c. A1:J10
d. A1:E22
Answer: c
Reference: The Simulation Process
Difficulty: Easy
Keywords: random number, Excel simulation
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18. To generate 80 random numbers in an Excel simulation, the “=RAND()” function is first
typed into the C2 cell on an Excel spreadsheet. C2 is then copied and pasted in a rectangular
area on the spreadsheet to cover the cells:
a. C2:G13
b. C2:J11
c. C2:F20
d. C2:D40
Answer: b
Reference: The Simulation Process
Difficulty: Moderate
Keywords: random number, Excel simulation
19. 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. .
Answer: a
Reference: The Simulation Process
Difficulty: Moderate
Keywords: random number, Excel simulation
20. The following table shows the probability of demand for automobiles used in an Excel
simulation.
The “= RAND()” function results in a random number for week #1 of 0.2239. The “=
VLOOKUP” function is used with the table above to generate a random car demand for week
#1. The resulting random car demand for this week is:
a. 1 car.
b. 2 cars.
c. 3 cars.
d. 4 cars.
Answer: b
Reference: The Simulation Process
Difficulty: Moderate
Keywords: random number, Excel simulation, VLOOKUP
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21. The following table shows the probability of demand for automobiles used in an
Excel simulation.
PROBABILITY OF LOWER RANGE CAR
DEMAND PROBABILITY DEMAND
0.08 0.00 0
0.10 0.08 1
0.20 0.18 2
0.35 0.38 3
0.15 0.73 4
0.12 0.88 5
1.00
The “= RAND()” function results in a random number for week #1 of 0.1705. The “=
VLOOKUP” function is used with the table above to generate a random car demand for week
#1. The resulting random car demand for this week is:
a. 1 car.
b. 2 cars.
c. 3 cars.
d. 4 cars.
Answer: a
Reference: The Simulation Process
Difficulty: Moderate
Keywords: random number, Excel simulation, VLOOKUP
22. The following table shows the probability of demand for automobiles used in an
Excel simulation.
PROBABILITY OF LOWER RANGE CAR
DEMAND PROBABILITY DEMAND
0.08 0.00 0
0.10 0.08 1
0.20 0.18 2
0.35 0.38 3
0.15 0.73 4
0.12 0.88 5
1.00
The “= RAND()” function results in a random number for week #1 of 0.7587. The “=
VLOOKUP” function is used with the table above to generate a random car demand for week
#1. The resulting random car demand for this week is:
a. 1 car.
b. 2 cars.
c. 3 cars.
d. 4 cars.
Answer: d
Reference: The Simulation Process
Difficulty: Moderate
Keywords: random number, Excel simulation, VLOOKUP
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23. Which one of the following statements about simulation analysis is FALSE?
a. If a result is statistically significant, it is always managerially significant.
b. Simulation analysis is a form of hypothesis testing.
c. In simulation, dependent variables reflect the values of both the decision variables and the
uncontrollable variables.
d. Statistical methods require the replication of simulation runs.
Answer: a
Reference: The Simulation Process
Difficulty: Hard
Keywords: simulation, statistically significant, managerially significant
24. 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.
Answer: b
Reference: Computer Simulation
Difficulty: Moderate
Keywords: steady state
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Supplement B Simulation
Scenario B.1
SimQuick is being used to simulate the following bank process:
Buffer
Entrance Buffer Work Station Served
Door Line Teller Customers
Customer arrivals at the Entrance Door of the bank with an average time between arrivals of
2.5 minutes. The Line Buffer holds 6 customers. If a customer arrives and the buffer line is
filled, the customer leaves. The Work Station Teller’s processing time per customer is
normally distributed, with a mean of 3.0 minutes and a standard deviation of 0.5 minutes. The
Served Customer Buffer in the flow chart is used to count the number of customers processed
during the period simulated. A 2-hour period was simulated.
Served
Buffer Customers Final inventory 36.85
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27. Use the information in Scenario B.1. Approximately how many total customers arrived
during the 2-hour period simulated?
a. 42
b. 38
c. 44
d. 48
Answer: d
Reference: Computer Simulation
Difficulty: Moderate
Keywords: SimQuick
28. Use the information in Scenario B.1. Approximately what percentage of total customers who
arrived during the 2-hour period found the buffer full and were not able to enter?
a. 87%
b. 13%
c. 94%
d. 6%
Answer: b
Reference: Computer Simulation
Difficulty: Moderate
Keywords: SimQuick
29. Use the information in Scenario B.1. Approximately how much time did the average
customer who entered the system spend waiting in line?
a. 9.75 minutes
b. 3.08 minutes
c. 5.85 minutes
d. 3.98 minutes
Answer: a
Reference: Computer Simulation
Difficulty: Moderate
Keywords: SimQuick
30. Use the information in Scenario B.1. On average, approximately how many customers were
waiting in line during the 2-hour simulation period?
a. 5
b. 4
c. 3
d. 2
Answer: c
Reference: Computer Simulation
Difficulty: Moderate
Keywords: SimQuick
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31. The arrival of customers at a lemonade stand is modeled in SimQuick using a(n):
a. entrance block.
b. buffer block.
c. workstation block.
d. decision point.
Answer: a
Reference: Computer Simulation
Difficulty: Moderate
Keywords: SimQuick, entrance block
32. A patient’s interminable wait for the first available physician is modeled in SimQuick using
a(n):
a. entrance block.
b. buffer block.
c. workstation block.
d. decision point.
Answer: b
Reference: Computer Simulation
Difficulty: Moderate
Keywords: SimQuick, buffer block
33. ____________ is the act of reproducing the behavior of a system using a model that describes
the processes of the system.
Answer: Simulation
Reference: Reasons for Using Simulation
Difficulty: Easy
Keywords: simulation model, system behavior
34. ____________ 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.
Answer: Time compression
Reference: Reasons for Using Simulation
Difficulty: Moderate
Keywords: time compression
36. The two approaches to data collection for simulation are ____________ and ____________.
Answer: statistical sampling, historical search
Reference: The Simulation Process
Difficulty: Moderate
Keywords: statistical sampling, historical search, data collection
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37. A number that has the same probability of being selected as any other number is a(n)
____________.
Answer: random number
Reference: The Simulation Process
Difficulty: Moderate
Keywords: random number, probability
38. 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) ____________..
Answer: decision variable
Reference: The Simulation Process
Difficulty: Moderate
Keywords: decision variable, controlled
39. ____________ are random events that the decision maker cannot control.
Answer: Uncontrollable variables
Reference: The Simulation Process
Difficulty: Moderate
Keywords: uncontrollable variable, random
40. ____________ occurs when the simulation is repeated over enough time that the average
results for performance measures remain constant.
Answer: Steady state
Reference: Computer Simulation
Difficulty: Moderate
Keywords: steady state
SHORT ANSWERS
41. What is the difference between a waiting line model as described in Supplement C and a
simulation model of a waiting line problem?
Answer: The waiting line model describes the operating characteristics of interest with
known equations. The simulation model actually mimics the arrival of customers and
their service, empirically calculating the operating characteristics.
Reference: Reasons for Using Simulation
Difficulty: Moderate
Keywords: simulation model, waiting line model
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43. What are the motivations for using simulation for analyzing processes?
Answer: Simulation models are useful when waiting line models are too complex. When
the relationship between variables is nonlinear, or when there are too many variables or
constraints to handle with optimizing approaches, simulation is an attractive option.
Simulation can be used to conduct experiments without disrupting the real system.
Simulation can also be used to discover operating characteristics of a system in much less
time than the data could be gathered from the real system. Finally, simulation can be
used to sharpen managerial decision making through gaming.
Reference: Reasons for Using Simulation
Difficulty: Moderate
Keywords: simulation model, time compression, waiting line model
44. 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 simulation run to the next as different events are simulated.
Uncontrolled variables are random events that the decision maker cannot control. Both
are functions of random numbers in the simulation model, but the decision maker realizes
that the uncontrolled variables, such as weather, customer arrival patterns, state of the
economy, and so on are outside his influence. Examples will vary.
Reference: Reasons for Using Simulation
Difficulty: Moderate
Keywords: decision variable, uncontrolled variable
PROBLEMS
Buffer
Entrance Buffer Work Station Served
Door Line Teller Customers
Customers arrive at the Entrance Door of the bank with an average time between arrivals
of 2.5 minutes The Line Buffer holds 6 customers. If a customer arrives and the buffer line
is filled, the customer leaves. The Work Station Teller’s processing time per customer is
normally distributed, with a mean of 3.0 minutes and a standard deviation of 0.5 minutes.
The Served Customer Buffer in the flowchart is used to count the number of customers
processed during the simulation period. A 2-hour period is to be simulated and the
simulation should be repeated 30 times. Determine:
a) The number of customers served during the 2-hour period;
b) The percentage of customers who arrived at the bank and left because the buffer line
was full;
c) The utilization of the teller (% of time working) during the 2-hour period;
Answer: The Model View of the completed elements for the simulation is shown on the
following page, followed by the results of the simulation
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Model View
Simulation controls:
Entrances:
1
Name Door
Average time between arrivals 2.5
Num. objects per arrival 1
Output
destination(s)
Line
Work Stations:
1
Name
Teller
Working
time Nor(3,.5)
Output # of output Resource Resource
# units needed
destination(s) objects name(s)
Served Customers 1
Buffers:
1 2
Served
Name Line Name Customers
Capacity 6 Capacity Unlimited
Initial #
Initial # objects 0 objects 0
Output Output Output Output
group destination(s)
destination(s) size group size
Teller 1
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Supplement B Simulation
Simulation Results
Work
Station(s) Teller Final status NA
Final inventory (int. buff.) 0.00
Mean inventory (int.
buff.) 0.00
Work cycles started 37.63
Fraction time working 0.93
Served
Customers Objects leaving 0.00
Final inventory 36.63
Minimum inventory 0.00
Maximum inventory 36.63
Mean inventory 17.23
a) The number of customers served is the final inventory in the Served Customers
Buffer: 36.63.
b) The service level (% of customers served) is 88%. The percent who balked (left
without being served is 1.00 – 0.88 = 12%.
c) The teller’s utilization level is shown as the “Fraction time working” under Work
Station Teller = 0.93 or 93%.
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46. Refer to the bank process model in problem #45. The Marketing Department for the bank has
decided to run a special promotion for new customers that will increase the number of
customers arriving at the bank. The new arrival rate is expected to be an average time
between arrivals of 2.0 minutes instead of the current average time between arrivals of 2.5
minutes. With the potential increase in business, the bank manager is concerned about the
number of customers who will arrive and leave because the line is full (with 6 customers) and
the average wait time in line at the bank. All other parameters of the model remain the same.
Using SimQuick, estimate the new arrive and immediately leave rate and average time in
line. Should the manager be concerned?
Answer: In the SimQuick model used for problem #45, the Entrance Door Time Between
Arrivals is revised to an average time between arrivals of 2.0 minutes and the model is run
again:
Simulation Results
Work
Station(s) Teller Final status NA
Final inventory (int. buff.) 0.00
Mean inventory (int.
buff.) 0.00
Mean cycle time (int.
buff.) 0.00
Work cycles started 39.37
Fraction time working 0.98
Fraction time blocked 0.00
Served
Customers Objects leaving 0.00
Final inventory 38.37
Minimum inventory 0.00
Maximum inventory 38.37
Mean inventory 18.45
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Supplement B Simulation
47. Refer to the bank process model in problem #45. The bank’s process improvement group has
developed a number of process and technology changes that will improve the Teller’s process
rate per customer from a mean of 3.0 minutes to 2.5 minutes (standard deviation remains at
0.5 minutes). The Bank Manager wants to determine if the improved process rate, along with
the special promotion for new customers, will allow the “arrive and immediately leave” rate
and average customer wait time in line achieved in problem #45 to still be met (12% balk
rate, 9.95 minutes in line). If so, the manager will implement the process and technology
changes and allow the special promotion to proceed. Using SimQuick, estimate the new
arrive and immediately leave rate and average time in line. What decision should the manager
make?
Answer: In the SimQuick model used for problem #45, the Entrance Door Time Between
Arrivals is revised to an average time between arrivals of 2.0 minutes and the Work Station
Teller’s Working Time is revised to a process time that has a normal distribution, with a
mean of 2.5 minutes and a standard deviation of 0.5 minutes. All other parameters remain
the same, and the model is run again (an abbreviated results summary is shown):
Simulation Results
Work
Station(s) Teller Work cycles started 46.57
Fraction time working 0.95
Served
Customers Final inventory 45.57
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Supplement B Simulation
Results show an Entrance Door service level of approximately 88%; therefore, the arrive
and immediately leave rate has decreased to approximately 12%, the same “balk” rate as
in problem #45.
In addition, the average time in line per customer has decreased to 8.05 minutes, almost 2
minutes per customer less than in problem #45.
The Bank Manager should implement the process changes and the new promotion,
recognizing that her arrive and immediately leave rate is no greater than it was originally,
and her customers will, on average, have approximately 2 minutes less wait time when
they come to the bank.
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