Deck 16: Simulation

Question 1

A table of uniformly distributed random numbers should be read

A)from left to right.
B)from top to bottom.
C)diagonally,starting from the top left corner and moving to the bottom right.
D)in any consistent sequence.

Answer 1

D

Question 2

Simulation is a trial-and-error approach to problem solving.

Answer 2

True

Question 3

The word "uniform" in the term "uniform random numbers" means

A)all the numbers have the same number of digits.
B)if one number is,say,10 units above the mean,the next number will be 10 units below the mean.
C)all the numbers are odd or all are even.
D)each number has an equal probability of being drawn.

Answer 3

D

Question 4

Which of the following statements is INCORRECT regarding the disadvantages of simulation?

A)Each simulation run only provides a sample of how the real system will operate.
B)The summary of the simulation data only provides estimates about the real system.
C)The process of developing a simulation model of a complex system can be time-consuming.
D)The larger the number of probabilistic inputs a system has,the less likely a simulation will provide the best approach for studying the system.

Question 5

Simulation

A)does not guarantee optimality.
B)is flexible and does not require the assumptions of theoretical models.
C)allows testing of the system without affecting the real system.
D)All of the alternatives are correct.

Question 6

Values for the probabilistic inputs to a simulation

A)are selected by the decision maker.
B)are controlled by the decision maker.
C)are randomly generated based on historical information.
D)are calculated by fixed mathematical formulas.

Question 7

Which of the following statements is INCORRECT regarding the advantages of simulation?

A)Simulation is relatively easy to explain and understand.
B)Simulation guarantees an optimal solution.
C)Simulation models are flexible.
D)A simulation model provides a convenient experimental laboratory for the real system.

Question 8

Simulation is an excellent technique to use when a situation is too complicated to use standard analytical procedures.

Question 9

Numerical values that appear in the mathematical relationships of a model and are considered known and remain constant over all trials of a simulation are

A)parameters.
B)probabilistic input.
C)controllable input.
D)events.

Question 10

A quantity that is difficult to measure with certainty is called a

A)risk analysis.
B)project determinant.
C)probabilistic input.
D)profit/loss process.

Question 11

The process of determining that the computer procedure that performs the simulation calculations is logically correct is called

A)implementation.
B)validation.
C)verification.
D)repetition.

Question 12

The number of units expected to be sold is uniformly distributed between 300 and 500.If r is a random number between 0 and 1,then the proper expression for sales is

A)200(r)
B)r + 300
C)300 + 500(r)
D)300 + r(200)

Question 13

A simulation model uses the mathematical expressions and logical relationships of the

A)real system.
B)computer model.
C)performance measures.
D)estimated inferences.

Question 14

The process of generating probabilistic inputs and computing the value of the output is called

A)simulation.
B)verification.
C)validation.
D)implementation.

Question 15

A value for probabilistic input from a discrete probability distribution

A)is the value given by the RAND()function.
B)is given by matching the probabilistic input with an interval of random numbers.
C)is between 0 and 1.
D)must be non-negative.

Question 16

Common features of simulations--generating values from probability distributions,maintaining records,recording data and summarizing results--led to the development of

A)Excel and Lotus.
B)BASIC,FORTRAN,PASCAL,and C.
C)GPSS,SIMSCRIPT,SLAM,and Arena
D)LINDO and The Management Scientist

Question 17

When events occur at discrete points in time

A)a simulation clock is required.
B)the simulation advances to the next event.
C)the model is a discrete-event simulation.
D)All of the alternatives are correct.

Question 18

In order to verify a simulation model

A)compare results from several simulation languages.
B)be sure that the procedures for calculations are logically correct.
C)confirm that the model accurately represents the real system.
D)run the model long enough to overcome initial start-up results.

Question 19

A simulation model used in situations where the state of the system at one point in time does not affect the state of the system at future points in time is called a

A)dynamic simulation model.
B)static simulation model.
C)steady-state simulation model.
D)discrete-event simulation model.

Question 20

If customer 2 has a service time of 1.6,and if customer 3 has an interarrival time of 1.1 and a service time of 2.3,when will customer 3's service be completed?

A)5.0
B)3.9
C)3.4
D)There is not enough information to answer.

Question 21

Simulation is an optimization technique.

Question 22

A discrete-event simulation reviews the status of the system periodically,whether or not an event occurs.

Question 23

For any waiting line system, (Average number of units in waiting line)= (Total waiting time)divided by (Total time of simulation).

Question 24

In a Monte Carlo simulation,each simulation trial is dependent upon the result of a previous trial.

Question 25

Each simulation run provides only a sample of how the real system will operate.

Question 26

Computer-generated random numbers are normally distributed over the interval from 0 to 1.

Question 27

Trials of a simulation show what would happen when values of the probabilistic input change.

Question 28

Using simulation to perform risk analysis is like playing out many what-if scenarios by randomly generating values for the probabilistic inputs.

Question 29

Verification is the process of ensuring that the simulation model provides an accurate representation of the real system.

Question 30

The drying rate in an industrial process is dependent on many factors and varies according to the following distribution.

a.Compute the mean drying time.
b.Using these random numbers,simulate the drying time for 12 processes.

c.What is the average drying time for the 10 processes you simulated?

Question 31

For the past 50 days,daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10).

a.Determine the relative frequency for each number of units sold.
b.Suppose that the following random numbers were obtained using Excel:

Use these random numbers to simulate 10 days of sales.

Question 32

Validation determines that the computer procedure is operating as it is intended to operate.

Question 33

The degree of risk is associated with the probability or magnitude of loss.

Question 34

To use Excel to generate a normally distributed random variable,you must know the mean and standard deviation of the distribution and have a random number between 0 and 1.

Question 35

A static simulation model is used in situations where the state of the system affects how the system changes or evolves over time.

Question 36

Computer-generated random numbers are normally distributed.

Question 37

In comparing different policies using simulation,one should use the same set of random numbers whenever possible.

Question 38

Simulation models that must take into account how the system changes or evolves over time are referred to as dynamic simulation models.

Question 39

Computer-generated random numbers are not technically random.

Question 40

The parameters of a simulation model are the controllable inputs.

Question 41

Seventy-five percent of calls arriving at a help line can be handled by the person who answers the phone,but the remaining 25% of them will need to be referred to someone else.Assume that every call requires one minute of attention by the person who answers the phone (either to answer the question or to figure out how the referral should be handled).Calls that are referred need an additional amount of time,as given in the table below.
Callers are served on a first come,first served basis,and are put on hold until the line is free.Use the random numbers to simulate what happens to 10 callers.(Use the random numbers in order - from left to right,first row first - as you need them. )What percentage of your callers needs to be referred? Of those who had to be referred,what is the average referral time?

Question 42

Greenfields is a mail order seed and plant business.The size of orders is uniformly distributed over the interval from $25 to $80.Use the following random numbers to generate the size of 10 orders.

Question 43

The time required to set up lighting for a portrait studio is uniformly distributed between 12 and 20 minutes.Use the following random numbers to generate the setup time for 10 customers.

Question 44

Susan Winslow has two alternative routes to travel from her home in Olport to her office in Lewisburg.She can travel on Freeway 5 to Freeway 57 or on Freeway 55 to Freeway 91.The time distributions are as follows:
Do a five-day simulation of each of the two combinations of routes using the random numbers below.Based on this simulation,which routes should Susan take if her objective is to minimize her total travel time?

Question 45

Three airlines compete on the route between New York and Los Angeles.Stanton Marketing has performed an analysis of first class business travelers to determine their airline choice.Stanton has modeled this choice as a Markov process and has determined the following transition probabilities.

a.Show the random number assignments that can be used to simulate the first class business traveler's next airline when her last airline is A,B,and C.
b.Assume the traveler used airline C last.Simulate which airline the traveler will be using over her next 25 flights.What percent of her flights are on each of the three airlines? Use the following random numbers,going from left to right,top to bottom.

SOLUTIONS TO PROBLEMS

Question 46

Estimates of the financial information for a new product show the following information:
Use the random numbers .51,.97,.58,.22,and .16 to simulate five trials.What is the net profit for each trial?

Question 47

As the owner of a rent-a-car agency you have determined the following statistics:
The gross profit is $40 per car per day rented.When there is demand for a car when none is available there is a goodwill loss of $80 and the rental is lost.Each day a car is unused costs you $5 per car.Your firm initially has 4 cars.
a.Conduct a 10-day simulation of this business using Row #1 below for demand and Row #2 below for rental length.

b.If your firm can obtain another car for $200 for 10 days,should you take the extra car?

Question 48

Arrivals to a truck repair facility have an interarrival time that is uniformly distributed between 20 and 50 minutes.Service times are normally distributed with mean 30 minutes and standard deviation 10 minutes.Develop a spreadsheet model to simulate the arrival of 100 trucks.Collect information on the time the repair facility is idle and on the average waiting time for trucks.

Question 49

An airline reservation system first asks customers whether they want to schedule a domestic or an international flight.Sixty-five percent of the reservations are for domestic flights.The time distribution of advance sales is also important,and it is given below.

a.Place the appropriate random number ranges in the tables above.
b.Set up and perform a simulation for three customers.Determine whether they want a domestic or international flight,and how far in advance the reservation is being made.Use random numbers from this list: .632 .715 .998 .671 .744 .021