Deck 10: Simulation Models

Question 1

Continuous simulation systems generally require the use of
differential equations to model alterations in system parameters.

Answer 1

True

Question 2

Monte Carlo simulation may be applied to problems in which a chance (random) process generates relevant occurrences.

Answer 2

True

Question 3

A computer-created random number generator uses a mathematical formula and produces pseudo-random numbers, which are not truly random.

Answer 3

True

Question 4

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.

Question 5

Simulation studies may be used to prove, or disprove, hypotheses regarding the system under investigation.

Question 6

When simulating a process with two random events (e.g., arrival time and service time) they each may be mapped using the same random number.

Question 7

In simulation studies, time may be represented as a fixed value or as a random variable.

Question 8

"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.

Question 9

Simulation can be used to model a functioning operation and study what would happen if we made extensive changes.

Question 10

A queuing system is generally simulated using the next event
approach but could be simulated with a fixed time approach.

Question 11

A simulation study:

A)evaluates options.
B)generates options.
C)generates optimal solutions.
D)evaluates parameters.

Question 12

The inverse distribution function expresses a value in terms of a cumulative distribution function.

Question 13

In random number mapping, the number assigned to correspond to the outcome of an event must be chosen randomly.

Question 14

Simulation models of queues are useful when the simplifying assumptions of the queuing model are invalid.

Question 15

A simulation of a queue always starts with an empty queue.

Question 16

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.

Question 17

Other than special purpose simulation languages (GPSS, SIMSCRIPT, etc.), the only general purpose programming language with
simulation capabilities is Excel.

Question 18

Crystal Ball Distribution Gallery includes both continuous and discrete distributions.

Question 19

Categories of simulation systems do not include those which are:

A)discrete.
B)continuous.
C)mixed discrete-continuous.
D)congruential.

Question 20

Performing additional simulation runs to estimate a value can reduce the confidence interval for that value.

Question 21

Why do you suppose many managers do not wholeheartedly accept the results of simulation studies?

Question 22

In the "next event" approach used in simulating inventory systems, the "events" typically may not correspond with:

A)inventory counts.
B)order placements.
C)order receipts.
D)customer arrivals.

Question 23

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.

Question 24

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.

Question 25

Why are computer-generated random numbers called pseudo-random
numbers?

Question 26

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.

Question 27

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?

Question 28

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?

Question 29

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.

Question 30

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.

Question 31

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.

Question 32

If the daily demand of x units has a probability of 0.20, will the corresponding "mapped" random numbers be 00-19?

Question 33

How does simulation differ from analytical techniques, such as queuing theory or linear programming?

Question 34

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.

Question 35

What are @Risk and Crystal Ball?

Question 36

What is wrong with this simulation flow chart?

Question 37

What is the difference between a simulation language, such as GPSS, and a simulator program, such as Extend?

Question 38

What proves the validity of a simulation model?

Question 39

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.

Question 40

Which of the following is not a simulator program?

A)Alpha/Sim.
B)SIMSCRIPT.
C)ProModel.
D)Extend.

Question 41

Repeat problem 2 using a next event approach.Assume the ship interarrival time is exponentially distributed with a mean of .5 days.

Question 42

To simulate an M/M/1 queue, how many random variable processes are needed? Identify what the random variables will represent.

Question 43

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.
$\begin{array}{ccccc}\text { Job}&\text { Predecessors}&\text {optimistic}&\text { Most Likely}&\text { Pessimistic }\\\text { A } & -- & 10 & 20 & 30 \\\text { B } & -- & 2 & 3 & 5 \\\text { C } & \text { B } & 5 & 8 & 10 \\\text { D } & \text { A } & 3 & 5 & 10 \\\text { E } & \text { C } & 1 & 2 & 4 \\\text { F } & \text { D } & 5 & 7 & 15 \\\text { G } & \text { D } & 5 & 7 & 15 \\\text { H } & \text { E, F } & 1 & 2 & 4 \\\text { I } & \text { H } & 15 & 20 & 30 \\\text { J } & \text { G. I } & 4 & 10 & 15\end{array}$
What is the probability that the project can be completed in 65 work days?

Question 44

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?

Question 45

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?

Question 46

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?

Question 47

Why is the next-event approach preferred for discrete simulations?

Question 48

In which Crystal Ball menu do you indicate the maximum number of trials and the desired confidence level?

Question 49

The explicit inverse distribution method and the interpolation method are used for what purpose?

Question 50

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 areTop-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?

Question 51

What does the Excel function FINV() do?

Question 52

What does Crystal Ball use as the default values for the normal distribution?

Question 53

What is the Excel function to generate a normally distributed random variable with mean 10 and variance 4?

Question 54

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: $\begin{array} { c c c } \text { Number of Ships per Day } & \text { Probability } \\0 & .10 & \\1 & .20 \\2 & .40 \\3 & .20 \\4 & .10\end{array}$
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.
$\begin{array} { c c } \text { Loading Time in Days } & \text { Probability } \\.5 & .35 \\1 & .45 \\1.5 & .15 \\2 & .05\end{array}$
Do a ten day fixed time simulation and estimate the average number of ships waiting at anchor for an available pierside berth and the average amount of time a ship must wait at anchor.