Deck 10: Simulation Modeling

Question 1

Which of the following is considered a disadvantage of simulation?

A)Simulation models do not allow for time compression.
B)Simulation models do not allow for what-if analysis.
C)Simulation models cannot emulate real systems.
D)Simulation models do not generate optimal solutions.
E)Simulation models are not unique.

Answer 1

D

Question 2

The Excel function =RAND()generates random numbers that are:

A)greater than 0
B)less than 1
C)between 0 and 0.9999
D)between -1 and 1
E)greater than 1

Answer 2

C

Question 3

A queuing system has an arrival rate of 5 customers per hour and a service rate of 8 customers per hour.You decide to build a simulation model to describe the service time per customer.The best appropriate distribution to use is:

A)triangular
B)exponential
C)normal
D)binomial
E)discrete uniform

Answer 3

B

Question 4

To establish a probability distribution,the relative frequency for each possible outcome of the variable is found by dividing the frequency of observation by the total number of observations.

Question 5

Simulation results can produce different solutions in repeated runs.

Question 6

John Smith is planning to refinance his home mortgage to take advantage of the lower current interest rates.As part of the refinancing application,the bank needs to appraise Mr.Smith's home.Mr.Smith expects an appraisal of at least $175,000 but no more than $250,000.All values between $175,000 and $250,000 have the same probability of being the actual appraised value.What is the appropriate distribution for simulating appraisal values?

A)continuous uniform
B)triangular
C)binomial
D)discrete uniform
E)normal

Question 7

Replicating a model about 20 times is adequate for the simulation results to be valid and useful.

Question 8

Simulation usually generates optimal solutions.

Question 9

What is the correct distribution for simulating the outcome of a single coin?

A)continuous uniform
B)triangular
C)binomial
D)exponential
E)normal

Question 10

What distribution is appropriate for simulating the event of rolling a single die?

A)continuous uniform
B)triangular
C)binomial
D)discrete uniform
E)normal

Question 11

If you simulate the event of tossing a coin 10 times,exactly 5 of the outcomes will be heads and 5 will be tails.

Question 12

What are output measures called in Crystal Ball?

A)forecasts
B)decisions
C)assumptions
D)random variables
E)cell preferences

Question 13

The uniform distribution can be discrete or continuous.

Question 14

The technique of randomly generating values for unknown elements in a model using random sampling is known as ________.

A)optimization
B)Markov analysis
C)discrete-event simulation
D)simulation gaming
E)Monte Carlo simulation

Question 15

A five-star hotel accepts 100 room reservations daily.For each reservation accepted,there is a 7% chance that the guest will not arrive.You decide to build a simulation model to describe the number of guests who will show up.The best appropriate distribution to use is:

A)normal
B)continuous uniform
C)discrete uniform
D)binomial
E)triangular

Question 16

Use this information and output to answer the following questions.
Rentals-R-Us specializes in 4WD car rentals.The number of rentals per month typically ranges between 10 and 50.You may assume equal probability for the number of rentals to assume any value in that range.The monthly operating costs for Rentals-R-Us can range anywhere from $2,000 to $4,000,with $3,000 being the most probable cost.Each rented vehicle generates $55 in revenues.You decide to build a simulation model in Crystal Ball to simulate monthly profits.
$$\begin{array} { | l | l | c | } \hline & { \text { A } } & \text { B } \\\hline 1 & \text { Rentals-R-Us } & \\\hline 2 & \text { Number of car rentals } & 50 \\\hline 3 & \text { Rental per car } & \$ 55 \\\hline 4 & \text { Monthly operating costs } & \$ 2,000 \\\hline 5 & \text { Profit or loss } & \$ 750 \\\hline\end{array}$$

-Refer to the table.Which cell(s)would be designated as the "Forecast cell"?

A)A5
B)B2
C)B3
D)B4
E)B5

Question 17

The sum of all previous probabilities up to the current probability is the ________.

A)cumulative probability
B)conditional probability
C)marginal probability
D)prior probability
E)posterior probability

Question 18

Use this information and output to answer the following questions.
Rentals-R-Us specializes in 4WD car rentals.The number of rentals per month typically ranges between 10 and 50.You may assume equal probability for the number of rentals to assume any value in that range.The monthly operating costs for Rentals-R-Us can range anywhere from $2,000 to $4,000,with $3,000 being the most probable cost.Each rented vehicle generates $55 in revenues.You decide to build a simulation model in Crystal Ball to simulate monthly profits.
$$\begin{array} { | l | l | c | } \hline & { \text { A } } & \text { B } \\\hline 1 & \text { Rentals-R-Us } & \\\hline 2 & \text { Number of car rentals } & 50 \\\hline 3 & \text { Rental per car } & \$ 55 \\\hline 4 & \text { Monthly operating costs } & \$ 2,000 \\\hline 5 & \text { Profit or loss } & \$ 750 \\\hline\end{array}$$

-Refer to the table.What is the appropriate distribution for the variable "Number of car rentals"?

A)continuous uniform
B)discrete uniform
C)normal
D)binomial
E)triangular

Question 19

Use this information and output to answer the following questions.
Rentals-R-Us specializes in 4WD car rentals.The number of rentals per month typically ranges between 10 and 50.You may assume equal probability for the number of rentals to assume any value in that range.The monthly operating costs for Rentals-R-Us can range anywhere from $2,000 to $4,000,with $3,000 being the most probable cost.Each rented vehicle generates $55 in revenues.You decide to build a simulation model in Crystal Ball to simulate monthly profits.
$$\begin{array} { | l | l | c | } \hline & { \text { A } } & \text { B } \\\hline 1 & \text { Rentals-R-Us } & \\\hline 2 & \text { Number of car rentals } & 50 \\\hline 3 & \text { Rental per car } & \$ 55 \\\hline 4 & \text { Monthly operating costs } & \$ 2,000 \\\hline 5 & \text { Profit or loss } & \$ 750 \\\hline\end{array}$$

-Refer to the table.What is the appropriate distribution for the variable "Monthly operating costs"?

A)continuous uniform
B)discrete uniform
C)normal
D)binomial
E)triangular

Question 20

Use this information and output to answer the following questions.
Rentals-R-Us specializes in 4WD car rentals.The number of rentals per month typically ranges between 10 and 50.You may assume equal probability for the number of rentals to assume any value in that range.The monthly operating costs for Rentals-R-Us can range anywhere from $2,000 to $4,000,with $3,000 being the most probable cost.Each rented vehicle generates $55 in revenues.You decide to build a simulation model in Crystal Ball to simulate monthly profits.
$$\begin{array} { | l | l | c | } \hline & { \text { A } } & \text { B } \\\hline 1 & \text { Rentals-R-Us } & \\\hline 2 & \text { Number of car rentals } & 50 \\\hline 3 & \text { Rental per car } & \$ 55 \\\hline 4 & \text { Monthly operating costs } & \$ 2,000 \\\hline 5 & \text { Profit or loss } & \$ 750 \\\hline\end{array}$$

-Refer to the table.What is the appropriate equation for cell B5?

A)=B2 - B4
B)=B3 - B4
C)=B4 - B2*B3
D)=B4 - B3*B2
E)=(B2*B3)- B4

Question 21

Use this information to answer the following questions.
The Gambler Hotel in Las Vegas has 300 rooms that each rent for $175 per night.For each reservation accepted,there is a 7% chance that the guest will not arrive.If the hotel overbooks,it incurs $220 for each reservation that is not honored.
Refer to the information above.Suppose that the hotel's manager believes that accepting 320 nightly reservations is a policy that the hotel should implement.Use Crystal Ball to estimate the average daily profit using the manager's policy.Use 1000 replications.

Question 22

A handyman specializes in fixing plumbing and electrical problems.Assume that 40% of the service calls that he gets relate to electrical problems,while 60% of the service calls relate to plumbing problems.On average,the time it takes to fix an electrical problem can range between 15 and 45 minutes,where all values between the minimum and maximum occur with equal likelihood.Moreover,the time it takes to fix a plumbing related problem can take a minimum of 15 minutes and a maximum of 60 minutes,where 30 minutes is the most probable time.
a.Use Crystal Ball to find the average time it takes the handyman to fix a given service call.Use 1000 replications.
b.What is the probability that it will take the handyman more than 45 minutes to complete a given service call?

Question 23

A binomial distribution can yield only two outcomes.

Question 24

Consider the event of tossing three coins.You are interested in computing the probability of getting three heads.Use Crystal Ball to simulate the event of tossing three coins 1000 times.
a.What is the theoretical probability of getting three heads?
b.What is the percentage of getting three heads using the 1000 simulated values?

Question 25

Cheap Rentals has collected the following information on the demand for compact cars over the last 30 days.

a.Use the historical data to estimate the probability distribution of demand for compact cars.
b.What is the theoretical expected demand?
c.Use Crystal Ball to simulate 1000 sample demand values.
d.Compare the mean of the 1000 sample values with the theoretical expected mean.

Question 26

An insurance company derives its revenues from its three primary business units: home insurance,auto insurance,and life insurance.The revenues for the year ending 2005,along with the potential growth rates per business unit for 2006 are illustrated below.

a.Use Crystal Ball to simulate total revenues for 2006.Run 1000 replications of the model to find the average revenues.
b.What is the probability that 2006 revenues will exceed $1.6 million?

Question 27

Excel uses the RAND()function to generate discrete values between 0 and 1.

Question 28

Monte Carlo simulation and operational gaming are the only two categories of simulation.

Question 29

Crystal Ball's CB.Custom function can be used to simulate discrete uniform random values.

Question 30

In a game of backgammon,your movement is based on the outcome that you get from rolling a pair of dice.Tossing a pair of sixes on the very first roll will give you a significant initial advantage over your opponent.Use Crystal Ball to determine the odds of rolling a pair of sixes in 1000 simulation runs.

Question 31

Consider a single deck of cards.Use Crystal Ball to determine the odds of drawing 2 aces without replacement.Use 1000 replications.

Question 32

An assembly plant has experienced the following daily absenteeism over the past 30 days.

a.Use the historical data to estimate the probability distribution of absenteeism.
b.What is the theoretical expected absenteeism?
c.Use Crystal Ball to simulate 1000 sample absenteeism values.
d.Compare the mean of the 1000 sample values with the theoretical expected mean.

Question 33

Consider the following game involving a single die.Someone offers to give you $1 if you toss a 1,$2 if you toss a 2,$3 if you toss a 3,etc.In other words,your earnings will correspond to the face value of the die.However,to play this game,each toss will cost you $2.50.You decide to use Crystal Ball to simulate your net earnings per toss based on 1000 simulation runs.What is your mean net earning per toss based on the simulated sample values?

Question 34

Use this information to answer the following questions.
The Gambler Hotel in Las Vegas has 300 rooms that each rent for $175 per night.For each reservation accepted,there is a 7% chance that the guest will not arrive.If the hotel overbooks,it incurs $220 for each reservation that is not honored.
Refer to the information above.Suppose that the manager wishes to examine the effect of different reservation levels on average profitability.In specific,the manager wishes to consider reservation levels of 280,290,300,310,and 320.Use Crystal Ball's Decision Table to find the reservation level that maximizes average profitability.Use 1000 replications.

Question 35

A simulation model may contain several output measures.

Question 36

In Excel,the function =NORMINV(RAND(),100,5)will return a normally distributed random number with a standard deviation of 100 and mean of 5.

Question 37

In Crystal Ball,probability distributions for input variables can be specified using either built-in functions or using Crystal Ball's menu.

Question 38

Joe Smith is a handyman who owns his own plumbing business.In a typical month,the number of service calls that he gets varies according to the following distribution:

His revenues per service call are normally distributed with a mean of $100 and a standard deviation of $20.His monthly expenses can range between a minimum of $1000 and a maximum of $1500,where all values between the minimum and maximum occur with equal likelihood.
a.Use Crystal Ball to simulate Mr.Smith's monthly profits.Run 1000 replications of the model.
b.What is the average monthly profit?

Question 39

Consider the following PERT network,along with the completion times for each activity,in days.Use Crystal Ball to enumerate the completion times of all paths in the network.Typically,the longest path in the network dictates the project completion time.Use 1000 replications.


a.What is the average project completion time?
b.What is the probability that the project completion time will exceed 50 days?

Question 40

A Decision Table is used in Excel to try at most 2 values automatically for a parameter in the model.

Question 41

Use this information to answer the following questions.
A supermarket stocks 150 apple pies each week.Weekly demand for apple pies ranges between 90 and 160 pies,all occurring with equal probability.Each unsold pie incurs an inventory carrying cost of $2.00.Unmet demand costs the supermarket $4.00 per pie.
Refer to the information above.Use Crystal Ball to find the average weekly costs (i.e. ,shortage and carrying costs)if the supermarket stocks 150 pies weekly.

Question 42

Use this information to answer the following questions.
A call center receives an average of 20 calls per minute.You may assume that the numbers of calls are independent of each other,and that the average number of calls remains the same for each minute interval.
Refer to the information above.
a.What type of distribution describes the number of calls received?
b.Use Crystal Ball to simulate the number of calls received per minute.Use 1000 replications.
c.What is the probability that the call center will receive more than 30 calls per minute?
d.What is the probability that the call center will receive less than 25 calls per minute?

Question 43

Use this information to answer the following questions.
A supermarket stocks 150 apple pies each week.Weekly demand for apple pies ranges between 90 and 160 pies,all occurring with equal probability.Each unsold pie incurs an inventory carrying cost of $2.00.Unmet demand costs the supermarket $4.00 per pie.
Refer to the information above.Suppose that the manager wishes to examine the effect of different stocking levels on the average weekly total costs.In specific,the manager wishes to consider stocking levels of 90 pies,110 pies,130 pies,and 150 pies.Use Crystal Ball's Decision Table to find the stocking level that minimizes average weekly total costs.Use 1000 replications.

Question 44

Use this information to answer the following questions.
The manager of an opera theater is concerned about overbooking one of his upcoming concerts.The theater has 300 seats,but sometimes there are empty seats.Tickets cost $50 per seat.Historical records demonstrate that about 9% of reservation holders do not show up.If the manager overbooks and more than 300 individuals show up,some of them will be given guaranteed reservations and VIP seats to the next coming show.Moreover,to keep his customers happy,the manager gives each individual who is bumped $20 worth of gift certificates.
Refer to the information above.Suppose that the manager wishes to examine the effect of different reservation levels on the average weekly total costs.In specific,the manager wishes to consider levels of 290,300,310,and 320.Use Crystal Ball's Decision Table to find the reservation level that maximizes average profit.Use 1000 replications.

Question 45

Daily demand for bananas at a grocery store is normally distributed with a mean of 100 lbs and standard deviation of 20.Use Excel to set up a Monte Carlo simulation of 12 months.

Question 46

Use this information to answer the following questions.
A call center receives an average of 20 calls per minute.You may assume that the numbers of calls are independent of each other,and that the average number of calls remains the same for each minute interval.
Refer to the information above.Suppose that the call center is interested in describing the time between successive telephone calls.You may assume that time has no effect on future telephone calls.
a.What type of distribution describes the time between successive telephone calls?
b.Use Crystal Ball to simulate the time between successive telephone calls.Use 1000 replications.
c.What is the average time between successive telephone calls?

Question 47

Suppose that someone offers you a job at a casino in Las Vegas with the following two options: you can either earn $68.00 per night working behind a change counter,or you can serve cocktail drinks.If the latter is chosen,your earnings potential is based on the number of patrons frequenting the casino each night.You can make $100 in tips on a busy night,$75 in tips on a normal night,and $50 in tips on a slow night.The probabilities of a busy,normal,or slow night are,respectively,0.4,0.3,and 0.3.
a.Which option maximizes your long-run average nightly earnings? Use Crystal Ball with 1000 replications.
b.How would your answer change if you can earn $85 per night working behind a counter?

Question 48

Use this information to answer the following questions.
The manager of an opera theater is concerned about overbooking one of his upcoming concerts.The theater has 300 seats,but sometimes there are empty seats.Tickets cost $50 per seat.Historical records demonstrate that about 9% of reservation holders do not show up.If the manager overbooks and more than 300 individuals show up,some of them will be given guaranteed reservations and VIP seats to the next coming show.Moreover,to keep his customers happy,the manager gives each individual who is bumped $20 worth of gift certificates.
Refer to the information above.The manager wishes to explore the impact on profitability if 310 reservations are accepted.Use Crystal Ball with 1000 replications.

Question 49

Suppose that IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.
a.Suppose that 1000 individuals took the IQ examination.Use Crystal Ball to simulate their scores.
b.What is the mean of the simulated IQ scores?
c.Suppose that being in the top 2% qualifies an individual as a genius.Using the simulated IQ scores,what should the IQ score be to qualify as a genius?

Question 50

When rolling a die once,what is the probability that the face of the die is odd? Use Crystal Ball to simulate the event of rolling a single die 1000 times in order to compute the requested probability.

Question 51

For the daily lottery in a given state,participants select three numbers between 0 and 9.You feel lucky and buy 1000 tickets from a 7-Eleven store.Suppose that the winning number is 999.Using Crystal Ball,simulate the outcomes of 1000 tickets to compute the odds of winning the lottery.Note that it is possible for 2 or more of your tickets to have the winning numbers.

Question 52

Suppose that the time needed to complete a final examination in a particular course is normally distributed with a mean of 60 minutes and a standard deviation of 10 minutes.
a.Use Crystal Ball to simulate 1000 test scores.
b.What is the probability of completing a test in less than 60 minutes?
c.What is the probability of completing a test between 50 minutes and 70 minutes?

Question 53

The probability that a sniper hits his target is 80%.If three snipers aim at the same target,use Crystal Ball to compute the odds that all three snipers will hit their target.Use 1000 replications.

Question 54

You have just graduated with an MBA degree and accepted your first job at the age of 25.You are thinking ahead for early retirement and you plan on saving $5000 at the end of each year.You expect each year's return to be modeled as a normal distribution with a mean of 10% and standard deviation of 2.5%.Suppose you intend to retire at the age of 55.Use Crystal Ball to simulate the ending investment value.Use 1000 replications.
a.What is the average amount of money that you will have at retirement?
b.What is the probability of having more than $1,000,000 at retirement?