Quantitative Analysis for Management, 11e (Render)
Chapter 14 Simulation Modeling
1) Simulation of a business or process is generally performed by building a mathematical model to represent the
process or system.
2) Simulation models are designed to generate optimal solutions, which can then be applied to real–world
situations.
3) A major advantage of using simulation techniques is to be able to study the interactive effect of individual
components/variables.
4) Despite the power of simulation, less than 20% of the largest U.S. corporations use simulation in corporate
planning.
5) One of the major advantages of simulation is “time compression,” i.e., the ability to study in a relatively short
period, activities that would, in reality, take place over a period of days, months, or even years.
6) To “simulate” is to try to duplicate the features, appearance, and characteristics of a real system.
7) While it is powerful, simulation is not considered to be a flexible quantitative analysis tool.
8) Simulation can use any probability distribution that the user defines; it does not require standard distributions.
9) One disadvantage of simulation is that it does not allow for “what–if?” types of questions.
10) Simulation models may contain both deterministic and probabilistic variables.
11) Monte Carlo simulation was developed as a quantitative technique by the great mathematician John von
Neumann during World War I.
12) Simulation models are limited to using standard probability distributions such as Poisson, exponential,
normal, etc.
13) The Monte Carlo simulation is used with variables that are probabilistic.
14) When using a random number generator, one should never start in the middle of the table of random
numbers.
15) If we are using a Monte Carlo simulation model, we should expect the model to produce the same results for
each set of random numbers used.
16) The four disadvantages of simulation are cost, its trial–and–error nature, time compression, and uniqueness.
17) The wider the variation among results produced by using different sets of random numbers, the longer we
need to run the simulation to obtain reliable results.
18) Simulation is very flexible. Thus, its solutions and inferences are usually transferable to other problems.
19) Simulation models are useful for economic order quantity problems with probabilistic demand and lead time.
20) A flow diagram is helpful in the logical coding procedures for programming a simulation process.
21) If, in a simple queuing or waiting line problem, we wish to know the maximum likely waiting time, or the
maximum likely length of the line, we must use a simulation model.
22) If, for a simple queuing or waiting line problem, we compare the solution from an analytical model with that
from a simulation, we will typically find them to be exactly the same.
23) The advantage of simulation over queuing or waiting line models is that simulation allows us to relax our
assumptions regarding arrival and service distributions.
24) Simulation of maintenance problems can help management analyze various staffing strategies based on
machine downtime and labor cost.
25) When establishing a probability distribution based on historical outcomes, the relative frequency for each
possible outcome of a variable is found by dividing the frequency of each outcome by the total number of
observations.
26) Operational gaming involves a single player competing with the computer simulated game.
Topic: OTHER SIMULATION ISSUES
27) There are three categories of simulation models: Monte Carlo, operational gaming, and systems simulation.
28) Validation relates to building the right model.
29) The following is not an advantage of simulation:
A) It allows for the study of what–if questions.
B) Each simulation model is unique.
C) It allows the study of interaction of components or variables to determine which are important.
D) It allows time compression.
E) None of the above
30) Simulation can be effectively used in many
A) inventory problems.
B) plant layout problems.
C) maintenance policy problems.
D) sales forecasting problems.
E) All of the above
31) Monte Carlo simulation was developed by ________.
A) John von Neumann
B) Eric von Brock
C) A.K. Erlang
D) P.K. Poisson
E) J.D. Monte Carlo
32) In assigning random numbers in a Monte Carlo simulation,
A) it is important to develop a cumulative probability distribution.
B) it is important to use a normal distribution for all variables simulated.
C) it is not important to assign probabilities to an exact range of random number intervals.
D) All of the above
E) None of the above
Table 14–1
A new young mother has opened a cloth diaper service. She is interested in simulating the number of diapers
required for a one–year– old. She hopes to use this data to show the cost effectiveness of cloth diapers. The table
below shows the number of diapers demanded daily and the probabilities associated with each level of demand.
Daily Demand Probability Interval of
Random Numbers
5 0.30 01–30
6 0.50 31–80
7 0.05 81–85
8 0.15 86–00
33) According to Table 14–1, if the random number 40 were generated for a particular day, what would the
simulated demand be for that day?
A) 5
B) 6
C) 7
D) 20
E) None of the above
34) According to Table 14–1, if the random number 96 were generated for a particular day, what would the
simulated demand be for that day?
A) 5
B) 6
C) 7
D) 8
E) None of the above
35) According to Table 14–1, what is the cumulative probability that demand is less than or equal to 7?
A) 0.85
B) 0.95
C) 0.80
D) 0.15
E) None of the above
Table 14–2
A pharmacy is considering hiring another pharmacist to better serve customers. To help analyze this situation,
records are kept to determine how many customers will arrive in any 10–minute interval. Based on 100 ten–
minute intervals, the following probability distribution has been developed and random numbers assigned to
each event.
Number of Arrivals Probability Interval of
Random Numbers
6 0.2 01–20
7 0.3 21–50
8 0.3 51–80
9 0.1 81–90
10 0.1 91–00
36) According to Table 14–2, the number of arrivals in any 10–minute period is between 6 and 10, inclusive.
Suppose the next three random numbers were 18, 89, and 67, and these were used to simulate arrivals in the next
three 10–minute intervals. How many customers would have arrived during this 30–minute time period?
A) 22
B) 23
C) 24
D) 25
E) None of the above
37) According to Table 14–2, the number of arrivals in any 10–minute period is between 6 and 10, inclusive.
Suppose the next three random numbers were 20, 50, and 79, and these were used to simulate arrivals in the next
three 10–minute intervals. How many customers would have arrived during this 30–minute time period?
A) 18
B) 19
C) 20
D) 21
E) None of the above
38) According to Table 14–2, the number of arrivals in any 10–minute period is between 6 and 10 inclusive.
Suppose the next 3 random numbers were 02, 81, and 18. These numbers are used to simulate arrivals into the
pharmacy. What would the average number of arrivals per 10–minute period be based on this set of occurrences?
A) 6
B) 7
C) 8
D) 9
E) None of the above
Table 14–3
A pawn shop in Arlington, Texas, has a drive–through window to better serve customers. The following tables
provide information about the time between arrivals and the service times required at the window on a
particularly busy day of the week. All times are in minutes.
Time Between Arrivals Probability Interval of
Random Numbers
1 0.1 01–10
2 0.3 11–40
3 0.4 41–80
4 0.2 81–00
Service Time Probability Interval of
Random Numbers
1 0.2 01–20
2 0.4 21–60
3 0.3 61–90
4 0.1 91–00
The first random number generated for arrivals is used to tell when the first customer arrives after opening.
39) According to Table 14–3, the time between successive arrivals is 1, 2, 3, or 4 minutes. If the store opens at 8:00
a.m., and random numbers are used to generate arrivals, what time would the first customer arrive if the first
random number were 02?
A) 8:01
B) 8:02
C) 8:03
D) 8:04
E) None of the above
40) According to Table 14–3, the time between successive arrivals is 1, 2, 3, or 4 minutes. The store opens at 8:00
a.m., and random numbers are used to generate arrivals and service times. The first random number to generate
an arrival is 39, while the first service time is generated by the random number 94. What time would the first
customer finish transacting business?
A) 8:03
B) 8:04
C) 8:05
D) 8:06
E) None of the above
41) According to Table 14–3, the time between successive arrivals is 1, 2, 3, or 4 minutes. The store opens at 8:00
a.m., and random numbers are used to generate arrivals and service times. The first 3 random numbers to
generate arrivals are 09, 89, and 26. What time does the third customer arrive?
A) 8:07
B) 8:08
C) 8:09
D) 8:10
E) None of the above
42) According to Table 14–3, the time between successive arrivals is 1, 2, 3, or 4 minutes. The store opens at 8:00
a.m., and random numbers are used to generate arrivals and service times. The first two random numbers for
arrivals are 95 and 08. The first two random numbers for service times are 92 and 18. At what time does the
second customer finish transacting business?
A) 8:07
B) 8:08
C) 8:09
D) 8:10
E) None of the above
Table 14–4
Variable Value Probability Cumulative Probability
0 0.08 0.08
1 0.23 0.31
2 0.32 0.63
3 0.28 0.91
4 0.09 1.00
Number of Runs 200
Average Value 2.10
43) According to Table 14–4, which presents a summary of the Monte Carlo output from a simulation of 200 runs,
there are 5 possible values for the variable of concern. If this variable represents the number of machine
breakdowns during a day, what is the probability that the number of breakdowns is 2 or fewer?
A) 0.23
B) 0.31
C) 0.32
D) 0.63
E) None of the above
44) According to Table 14–4, which presents a summary of the Monte Carlo output from a simulation of 200 runs,
there are 5 possible values for the variable of concern. If this variable represents the number of machine
breakdowns during a day, what is the probability that the number of breakdowns is more than 4?
A) 0
B) 0.08
C) 0.09
D) 1.00
E) None of the above
45) According to Table 14–4, which presents a summary of the Monte Carlo output from a simulation of 200 runs,
there are 5 possible values for the variable of concern. If random numbers between 01 and 100 are used to
generate values, then a random draw of 72 would produce a variable value of ________.
A) 0
B) 1
C) 2
D) 3
E) 4
46) Which of the following represents the primary reason simulation cannot be used for the classic EOQ model?
A) too many parameters involved
B) too many decision variables
C) EOQ models are probabilistic
D) EOQ models are deterministic
E) None of the above
47) Which of the following scenarios would require simulation for a queuing model?
A) Poisson arrival process
B) exponential service time
C) deterministic arrival process
D) deterministic service time
E) None of the above
48) Simulation models can be broken down into which of the following three categories?
A) Monte Carlo, queuing, and inventory
B) queuing, inventory, and maintenance policy
C) Monte Carlo, operational gaming, systems simulation
D) inventory, systems simulation, and operational gaming
E) None of the above