CHAPTER 10
SIMULATION MODELS
TRUE/FALSE QUESTIONS
1. Other than special purpose simulation languages (GPSS,
SIMSCRIPT, etc.), the only general purpose programming language with
2. Continuous simulation systems generally require the use of
3. In random number mapping, the number assigned to correspond to
4. Monte Carlo simulation may be applied to problems in which a
chance (random) process generates relevant occurrences.
5. A computer-created random number generator uses a mathematical
formula and produces pseudo-random numbers, which are not truly
6. Simulation studies may be used to prove, or disprove,
hypotheses regarding the system under investigation.
7. A queuing system is generally simulated using the next event
approach but could be simulated with a fixed time approach.
8. In simulation studies, time may be represented as a fixed
9. When simulating a process with two random events (e.g.,
arrival time and service time) they each may be mapped using the
10. Simulation models of queues are useful when the simplifying
11. A simulation of a queue always starts with an empty queue.
12. Crystal Ball Distribution Gallery includes both continuous and
13. The inverse distribution function expresses a value in terms
14. Performing additional simulation runs to estimate a value can
15. Simulation can be used to model a functioning operation and
MULTIPLE CHOICE QUESTIONS
1. A simulation study:
a. evaluates options.
b. generates options.
c. generates optimal solutions.
d. evaluates parameters.
2. “Increments” in a given simulation study may be measured by:
a. fixed times.
b. next events.
c. fixed times or next events.
d. fixed times and next events.
3. Categories of simulation systems do not include those which
are:
a. discrete.
b. continuous.
c. mixed discrete-continuous.
d. congruential.
4. In mapping random numbers to the outcomes of a simulated
event, the random numbers must be selected:
a. sequentially.
b. systematically.
c. randomly.
d. by any unbiased process.
5. Where the events to be simulated have a continuous probability
distribution, F(x) is employed. F(x) is:
a. P(X ≤ x).
b. P(X = x).
c. P(X ≥ x).
d. decumulative.
6. The sequence of numbers produced by a computer’s random number
generator:
a. will show autocorrelation.
b. is independent of the “seed” selected.
c. is derived by mathematical formula.
d. is genuinely random.
7. In conducting a hypothesis test using simulation results:
a. one may not be able to draw a firm conclusion regarding
the optimal policy.
b. the null hypothesis may be proved correct.
c. the alternate hypothesis reflects the simulation’s
estimated value(s).
d. the results (of the simulation) generate the null
hypothesis.
8. In simulating a queuing system:
a. multiple random number generators must be used.
b. service times cannot be constant.
c. the queue discipline must be first-come, first-served.
d. arrivals may follow a uniform distribution.
9. In the “next event” approach used in simulating inventory
systems, the “events” typically may not correspond with:
10. An inventory system may be simulated using:
a. a variable-time approach only.
b. a fixed-time approach only.
c. a next-event approach only.
d. a fixed-time or next-event approach.
11. Simulation analysis:
a. is often used in conjunction with mathematical analysis.
b. is time consuming and costly.
c. generates verifiably optimal solutions.
d. provides insights into relationships among variables.
12. Which of the following is not a simulator program?
a. Alpha/Sim.
b. SIMSCRIPT.
c. ProModel.
d. Extend.
13. Which of the following statements is true?
a. Zero should not be used as a seed value.
b. Using the same seed value for simulation of different
options does not reduce the amount of work necessary to
achieve the desired statistical precision.
c. Using the same seed value will produce the same set of
random numbers in exactly the same order.
d. The RAND() function accepts a seed value as an input
parameter.
14. Which Crystal Ball menu item do you use to assign a
probability distribution to a cell?
a. Define Assumption.
b. Define Decision.
c. Define Forecast.
d. Cell Preference.
15. Crystal Ball is:
a. a standalone simulation program.
b. a specialized simulation language.
c. an Excel add-in for simulation.
d. a graphic simulator program.
SHORT ANSWER QUESTIONS
1. Pseudo-random numbers are often generated in groups, such as
07967 45929 85113 36308. What determines which specific digits to
use in random number mapping?
2. If the daily demand of x units has a probability of 0.20, will
the corresponding “mapped” random numbers be 00-19?
3. Why are computer-generated random numbers called pseudo-random
numbers?
4. If we are simulating a queuing system, is it permissible to
use the same random number to describe both an interarrival time and
a customer’s service time?
5. Why do you suppose many managers do not wholeheartedly accept
the results of simulation studies?
6. What proves the validity of a simulation model?
7. How does simulation differ from analytical techniques, such as
queuing theory or linear programming?
8. What are @Risk and Crystal Ball?
9. What is the difference between a simulation language, such as
GPSS, and a simulator program, such as Extend?
10. What is wrong with this simulation flow chart?
11. Why is the next-event approach preferred for discrete
simulations?
12. The explicit inverse distribution method and the interpolation
method are used for what purpose?
13. What is the Excel function to generate a normally distributed
random variable with mean 10 and variance 4?
14. What does the Excel function FINV() do?
15. To simulate an M/M/1 queue, how many random variable processes
are needed? Identify what the random variables will represent.
16. In which Crystal Ball menu do you indicate the maximum number
of trials and the desired confidence level?
17. What does Crystal Ball use as the default values for the
normal distribution?
FORMULATION/SOLUTION/ANALYSIS QUESTIONS
1. Titus Tronix is currently having a consumer electronics
clearance sale. The store presently has 10 Gadzooks video cassette
recorders on sale. Five are Standard, three are Economy, and two are
Top-of-Line. Each day the firm expects between 0 and 3 customers
interested in buying a VCR to arrive at the store according to the
following probability distribution:
P(0 arrivals) = .15
P(1 arrivals) = .40
P(2 arrivals) = .25
P(3 arrivals) = .20
For each customer interested in buying a VCR, there is a seventy
percent chance that the customer will want to purchase one of the
sale-priced Gadzooks models. Titus knows from past experience that
sixty percent will want a Standard, twenty-five percent will want
the Economy, and fifteen percent will desire the Top-of-Line. If
the store is sold out of a particular price-level model, the
customer who wanted it will leave the store without buying any
other.
Set up a model which will simulate five days of VCR sales at Titus.
Use any set of random numbers, but clearly indicate how they were
selected. What is your estimate of Titus’ remaining inventory of the
three Gadzooks models, at the end of five days?
2. Papagayo Rum is produced on the island of the same name, and
its entire output is exported by ship. There is only one pier
capable of accommodating the freighters, which arrive empty, are
then loaded with their cargo of rum, and then depart. The pier may
service at most two ships at a time.
Cargo ships arrive randomly according to the following distribution:
Number of Ships per Day Probability
0 .10
1 .20
2 .40
3 .20
4 .10
If the pier is occupied by two freighters, a subsequent arrival
drops anchor in the harbor and awaits its turn. The time required
to load a ship is also variable, depending on the vessel’s capacity
and configuration as well as available dockside manpower and
equipment.
3. Repeat problem 2 using a next event approach. Assume the ship
interarrival time is exponentially distributed with a mean of .5
days.
4. Jasper’s is licensed by the state to perform emission testing
on passenger vehicles. Should a vehicle not pass the test, Jasper’s
is also authorized, if requested, to perform the work necessary to
remedy the problem.
5. Consider a video store carrying two brands of satellite
dishes, Sony and RCA. Each day between 0 and 4 customers arrive to
purchase these dishes with the following probability distribution:
# of Customers Probability
0 .15
1 .30
2 .25
3 .20
4 .10
There is a 70% chance that a customer will want a Sony dish and a
30% chance that the customer will want an RCA dish. If a customer
wants a Sony dish but the store is sold out, there is a 40% chance
that the customer will purchase the RCA dish instead, a 40% chance
that the customer will place a backorder, and a 20% chance that the
sale will be lost. If the customer wants an RCA dish but the store
is sold out, there is a 50% chance the customer will place a
backorder and a 50% chance that the sale will be lost.
6. Office Max sells both Eureka and Hammerstrom paper. Each day,
as many as five customers come in to purchase boxes of these papers
(a box contains 10 reams). The distribution of customer arrivals is
as follows:
# of Customers Probability
0 .10
1 .20
2 .35
3 .20
4 .10
5 .05
7. GoodFriend Inc. plans to upgrade its accounting software. The
main activities for the project are:
A. Evaluate available products.
B. Determine the hardware requirements.
C. Order and obtain the hardware.
D. Order and obtain the software.
E. Set up the hardware.
F. Train the IT staff to implement and support the software.
G. Train the end users.
H. Install the software.
I. Customize the software.
J. Test the system.
The following table indicates the PERT estimates in work days.
Job
Predecessors
Optimistic
Most Likely
Pessimistic
A
—
10
20
30
B
—
2
3
5
C
B
5
8
10
D
A
3
5
10
E
C
1
2
4
F
D
5
7
15
G
D
5
7
15
H
E, F
1
2
4
I
H
15
20
30
J
G, I
4
10
15
What is the probability that the project can be completed in 65 work
days?
8. Simulate the post office function for eight hours on December
10, two weeks before Christmas. Arrivals are Poisson distributed at
an average of one per minute. Service time is exponential with a
mean of 3 minutes. Six servers are available. What is the average
length of the queue?
9. Simulate the elevator operation at the Bank of Liberty
building. Between 7:00 AM and 7:00 PM, 1440 people arrive daily at
the first floor of the 20 story structure. Assume a uniform
distribution of both arrivals and destinations (which floor).
Assume each person stays exactly one hour. Everyone leaves the
building by 8:00 PM. The elevators hold 20 people, travel at 6
floors/minute, and require 30 seconds for each stop. How many
elevators does the building require if no one is to wait more than 5
minutes?
10. Muchobucks Funding, a venture capital company, invests in a
high-tech, pre–IPO startup. Assume the startup has an exponential
distribution of income with a mean of $500,000 per year and one
million dollars in expenses. That is, the company is expected to
lose half a million dollars each year. Once a startup loses $2
million, Muchobucks pulls the plug, and the startup goes out of
business. How long will the average startup last?