Deck 12: Introduction to Simulation Using Analytic Solver Platform

Question 1

One of Analytic Solver Platform's amazing capabilities is its ability to perform interactive simulation.

Answer 1

True

Question 2

Exhibit 12.2
The following questions use the information below.
The owner of Fix-a-dent Auto Repair wants to study the growth of his business using simulation. He is interested in simulating the number of damaged cars and the amount of damage to the cars each month. He currently repairs 100 cars per month and feels the change in number of cars can vary uniformly between a decrease of as much as 3% and an increase of up to 5% (average change of 1%). The dollar value of the damage to the cars is a normally distributed random variable with a mean of $3,000 and a standard deviation of $500. The average repair bill has been increasing steadily over the years and the owner expects the mean repair bill will increase by 1% per month. A spreadsheet model to simulate the problem has been run 300 times. A part of the simulation statistics output from Risk Solver Platform (RSP)and a spreadsheet for computing confidence intervals follows.
Using the information in Exhibit 12.2, what formula should go in cell B12 of the Confidence Intervals spreadsheet to compute the upper limit on a 95% confidence interval for the population proportion below 90%?

A) =B10+1.96*B10*(1-B10)/SQRT(B2)
B) =B10+1.96*SQRT(B10*(1-B10)/B2)
C) =B10+1.96*SQRT(B10*(1-B10)*B2)
D) =B10+1.96*B10*(1-B10)/B2

Answer 2

=B10+1.96*SQRT(B10*(1-B10)/B2)

Question 3

​The term "risk" also implies the potential for loss.

Answer 3

True

Question 4

To perform simulation in a spreadsheet, we must first place a random number generator (RNG) formula in each cell that represents a random, or uncertain, independent variable.

Question 5

The educational version of Analytic Solver Platform has no limit on the number of trials per simulation.

Question 6

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
The average demand is 4.45 cases per day. Using the information in Exhibit 12.3, what formula should go in cell H4 to determine the average lost sales?

A) =H3*4.45*10*30
B) =(1-H3)*4.45*10
C) =(1-H3)*4.45*30
D) =(1-H3)*4.45*10*30

Question 7

In the face of uncertainty, some people react with paralysis, or they do exhaustive research to avoid making a decision.

Question 8

The best-case analysis approach to risk analysis

A) is optimistic
B) is pessimistic
C) is most likely
D) is likely to produce good outcomes

Question 9

If you have historical data for any of the random variables in your model, you can use this dialog to instruct Analytic Solver Platform to automatically identify and suggest appropriate probability distributions for your data.

Question 10

The historical data itself can be sampled from using Analytic Solver Platform's PsiDisUniform( ), PsiResample( ), PsiSip( ) or PsiSlurp( ) functions.

Question 11

If chance or uncertainty is present in a system then there is an element of ____ in the decision-making problem.

A) danger
B) security
C) risk
D) difficulty

Question 12

In general there are two primary issues involved in risk. What are these two issues?

A) Validation of spreadsheet model and setting up for the simulation.
B) Uncertainty of the outcome and magnitude of the potential loss.
C) Maximum amount of profit made and the probability of a maximum profit.
D) Maximum amount of loss incurred and the likelihood of that loss.

Question 13

In running simulations under Analytic Solver Platform it is desirable to use more simulation runs because

A) confidence level regarding the decision precision is improved
B) point estimates are more accurate
C) simulation run length is decreased
D) cost is decreased

Question 14

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Using the information in Exhibit 12.3, what formula should go in cell H8 to determine if an order should be placed?

A) =IF(G8<$D$3,1,0)
B) =IF(G8>$D$3,1,0)
C) =IF(G8<$D$3,0,1)
D) =IF(G8<$D$4,1,0)

Question 15

A random variable is

A) a variable whose value cannot be predicted with certainty
B) a parameter
C) a population variable
D) a sample variable

Question 16

Which Analytic Solver Platform function will generate random integer numbers between 2 and 8?

A) =PsiIntUniform(2, 8)
B) =PsiDiscrete(2, 8)
C) =PsiUniform(2, 8)
D) =PsiRandom(2, 8)

Question 17

What is the correct Analytic Solver Platform function for generating random numbers from the following distribution on the number of children in families (assume a reference to the current worksheet).

A) =PsiCustom(A2:A6,B2:B6)
B) =PsiRandom(A2:A6,B2:B6)
C) =PsiDiscrete(A2:A6,B2:B6)
D) =PsiUniform(A2:A6,B2:B6)

Question 18

Simulation is used to

A) find possible worst case values for the dependent variable(s).
B) find worst case and best case values for the dependent variable(s).
C) find distribution information for the dependent variable(s).
D) find median values for the dependent variable(s).

Question 19

Exhibit 12.4.
The following questions use the information below.
The manager of a Washington, DC sightseeing tour company is concerned about overbooking for one of his bus tours. The bus has 15 seats but sometimes there are empty seats. His records show that about 20% of ticket holders do not show up for their tour. Tickets cost $10 and are non-refundable. If the manager overbooks the tour and more than 15 passengers show up, some of them will be bumped to a later tour. This bumping costs the company $25 in various expenses to keep the customer happy until the next tour. The manager wants to see what happens to profits if 18 reservations are accepted.
Using the information in Exhibit 12.4, what formula should go in cell C14 of the worksheet to determine the Cost of Bumping Passengers?

A) =C5*MAX(C10-C4,0)
B) =C5*MAX(C10,0)
C) =MAX(C10-C4,0)
D) =C5*MAX(C10,C4)

Question 20

Several techniques are available to help managers analyze risk. Three of the most common are best-case/worst-case analysis, what-if analysis, and simulation. Of these methods, what-if analysis the most powerful.

Question 21

Methods for analyzing risk that are discussed in the textbook include

A) best-case/worst case analysis
B) what-if analysis
C) simulation
D) all of the above

Question 22

Uncertainty

A) is the most difficult thing about decision-making
B) simplifies decision-making
C) is easy to capture with computers
D) requires the use of quantitative models for supporting decision-making

Question 23

Exhibit 12.1
The following questions use the information below.
The owner of Fix-a-dent Auto Repair wants to study the growth of his business using simulation. He is interested in simulating the number of damaged cars and the amount of damage to the cars each month. He currently repairs 100 cars per month and feels this can vary uniformly between a decrease of as much as 3% and an increase of up to 5% (average change of 1%) over the previous months. The dollar value of the damage to the cars is a normally distributed random variable with a mean of $3,000 and a standard deviation of $500. The average repair bill has been increasing steadily over the years and the owner expects the mean repair bill will increase by 1% per month. You have created the following spreadsheet to simulate the problem.
Using the information in Exhibit 12.1, what formula should go cell G5 to calculate the 80^th percentile of the empirical distribution of income?

A) =IF(RANK(D21) = 80, 1, 0)
B) None, use Excel Histogram on cell D21.
C) =IF(COUNTIF(D8:D19 > D21) ≥ 8, 1, 0)
D) =PsiPercentile(B21, .8).

Question 24

Which Analytic Solver Platform function will generate random numbers between 3 and 7 from a continuous uniform distribution?

A) =PsiConUniform(3, 7)
B) =PsiUniDist(3, 7)
C) =PsiUniform(3, 7)
D) =PsiTruncate(3, 7)

Question 25

Which of the following probability distributions are associated with discrete outcomes?

A) Gamma
B) Custom
C) Normal
D) Exponential

Question 26

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Using the information in Exhibit 12.3, what Analytic Solver Platform function should be used in cell I8 to determine the lead time for an order?

A) =PsiDiscrete($B$6:$B$8, $C$6:$C$8)
B) =PsiPoisson(Data!$B$6:$B$8,$Data!$C$6:$C$8)
C) =PsiBinomial(Data!$B$6:$B$8,$Data!$C$6:$C$8)
D) =PsiNormal($B$6:$C$8)

Question 27

Best case analysis is a(n) ____ view of the problem.

A) pessimistic
B) optimistic
C) risky
D) certain

Question 28

Which of the following distributions can be generated by Analytic Solver Platform?

A) Poisson
B) Normal
C) Weibull
D) All of these

Question 29

As the number of replicates in a simulation increases the width of a confidence interval computed from the simulation results will

A) decrease.
B) increase.
C) remain the same.
D) change depends on standard deviation.

Question 30

The PsiTarget(.) function in Analytic Solver Platform

A) returns the cumulative probability of a specified distribution cell being less or equal to the specified target value
B) returns the cumulative probability of a specified distribution cell being equal to or larger than the specified target value
C) returns the cumulative probability of a specified distribution cell being equal to the specified target value
D) returns the probability of a specified distribution cell being equal to the specified target value

Question 31

Exhibit 12.4.
The following questions use the information below.
The manager of a Washington, DC sightseeing tour company is concerned about overbooking for one of his bus tours. The bus has 15 seats but sometimes there are empty seats. His records show that about 20% of ticket holders do not show up for their tour. Tickets cost $10 and are non-refundable. If the manager overbooks the tour and more than 15 passengers show up, some of them will be bumped to a later tour. This bumping costs the company $25 in various expenses to keep the customer happy until the next tour. The manager wants to see what happens to profits if 18 reservations are accepted.
Using the information in Exhibit 12.4, what formula should go in cell C13 of the worksheet to determine the Opportunity Cost of Empty Seats?

A) =C5*MAX(C4,C10)
B) =C5*MAX(C4,0)
C) =MAX(C4-C10,0)
D) =C5*MAX(C4-C10,0)

Question 32

Using the information in Exhibit 12.1, what Analytic Solver Platform function should go in cell C8 and copied to cells C9:C19 to compute the average damage per car in the month?

A) =PsiNormal($C$3*$F$3^$A$8, $H$3)
B) =PsiNormal($C$3*$F$3^A8, $H$3)
C) =PsiNormal($C$3, $D$3*(1+$F$3)^A8)
D) =PsiNormal($C$3*(1+$F$3)^A8, $H$3)

Question 33

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Using the information in Exhibit 12.3, what formula should go in cell C9 and copied to C10:C21 of the MODEL sheet to compute units received?

A) =COUNT($J$8:J8,A9)*$D$4
B) =COUNTIF($J$8:J8,A8)*$C$4
C) =COUNTIF($J$8:J8,A9)*$D$5
D) =COUNTIF($J$8:J8,A9)*$D$4

Question 34

The benefit(s) of simulation discussed in the text is/are

A) gaining better insight into a problem
B) ability to make more informed decisions
C) eliminating the need to build a system with fine-tuning occurring after the launch
D) all of the above

Question 35

Using the information in Exhibit 12.3, what Analytic Solver Platform function should be used in cell D8 and copied to cells D9:D21 of the MODEL sheet to compute daily demand?

A) =PsiDiscrete($E$6:$E$13, $F$6:$F$13)
B) =PsiHypergeo($E$6:$F138)
C) =PsiBinomial($E$6, $F$13)
D) =PsiCustom(Data!$E$6, $F$13)

Question 36

What is a weakness of manual what-if analysis?

A) biased sample values of performance measures
B) hard to do many what-if scenarios
C) does not provide distribution information
D) all of these are weaknesses

Question 37

Worst case analysis is a(n) ____ view of the problem.

A) pessimistic
B) optimistic
C) risky
D) certain

Question 38

Some discrete distributions available in Analytic Solver Platform are

A) binomial
B) Poisson
C) Hypergeometric
D) all of the above

Question 39

Risk needs to be analyzed using models in order to

A) make decisions better than those based on informed guesses
B) obtain a feasible solution
C) obtain an optimal solution
D) confound the decision-making process

Question 40

Which of the following probability distributions are associated with continuous outcomes?

A) Poisson
B) Binomial
C) Custom
D) Triangular

Question 41

Which of the following best describes a random variable?

A) A spreadsheet input cell containing a random number generator.
B) The outcome of a simulation model.
C) Any variable whose value cannot be predicted with certainty.
D) All of these describe random variables.

Question 42

Exhibit 12.2
The following questions use the information below.
The owner of Fix-a-dent Auto Repair wants to study the growth of his business using simulation. He is interested in simulating the number of damaged cars and the amount of damage to the cars each month. He currently repairs 100 cars per month and feels the change in number of cars can vary uniformly between a decrease of as much as 3% and an increase of up to 5% (average change of 1%). The dollar value of the damage to the cars is a normally distributed random variable with a mean of $3,000 and a standard deviation of $500. The average repair bill has been increasing steadily over the years and the owner expects the mean repair bill will increase by 1% per month. A spreadsheet model to simulate the problem has been run 300 times. A part of the simulation statistics output from Risk Solver Platform (RSP)and a spreadsheet for computing confidence intervals follows.
Using the information in Exhibit 12.2, what is the worst case scenario for the Fix-a-dent company based on this output?

A) $1,747,464.94
B) $3,339,249.82
C) $4,122,024.01
D) $4,207,301.98

Question 43

In a what-if analysis the decision maker

A) changes the values of the uncertain input variables to see what happens to the performance measure being studied
B) assumes that all inputs are random variables
C) assumes that all outputs are deterministic
D) corrects for underestimated risk

Question 44

How should one determine which RNGs to employ in a spreadsheet simulation model?

A) Use the Analytic Solver Platform gallery and pick a distribution.
B) Generate thousands of samples and compare the resulting histogram to ensure the distribution is correct.
C) Solve the deterministic model repeatedly and use Analytic Solver Platform distribution fitting tools.
D) The distributions selected should represent the underlying pool of values expected to occur.

Question 45

Exhibit 12.1
The following questions use the information below.
The owner of Fix-a-dent Auto Repair wants to study the growth of his business using simulation. He is interested in simulating the number of damaged cars and the amount of damage to the cars each month. He currently repairs 100 cars per month and feels this can vary uniformly between a decrease of as much as 3% and an increase of up to 5% (average change of 1%) over the previous months. The dollar value of the damage to the cars is a normally distributed random variable with a mean of $3,000 and a standard deviation of $500. The average repair bill has been increasing steadily over the years and the owner expects the mean repair bill will increase by 1% per month. You have created the following spreadsheet to simulate the problem.
Using the information in Exhibit 12.1, what Analytic Solver Platform function should go in cell B8 to compute the number of cars repaired in the first month?

A) =PsiUniform($C$2*(1-$F$2), $C$2*(1+$H$2))
B) =PsiUniform($C$2*1-$F$2, $C$2*1+$H$2)
C) =PsiUniform($C$2-(1-$F$2), $C$2+(1+$H$2))
D) =PsiUniform($C$2+(1-$F$2), $C$2+(1+$H$2))

Question 46

The Analytic Solver Platform is a good simulation tool because

A) it is difficult to use
B) it provides several polymorphic spreadsheet interpreter "psi" functions to facilitate Excel calculations
C) it has a limited choice of statistical distributions making it difficult to approximate reality
D) it requires a standalone platform operating independently of Excel

Question 47

Common continuous distributions available in Analytic Solver Platform are

A) exponential
B) Normal
C) truncated Normal
D) all of the above

Question 48

Exhibit 12.4.
The following questions use the information below.
The manager of a Washington, DC sightseeing tour company is concerned about overbooking for one of his bus tours. The bus has 15 seats but sometimes there are empty seats. His records show that about 20% of ticket holders do not show up for their tour. Tickets cost $10 and are non-refundable. If the manager overbooks the tour and more than 15 passengers show up, some of them will be bumped to a later tour. This bumping costs the company $25 in various expenses to keep the customer happy until the next tour. The manager wants to see what happens to profits if 18 reservations are accepted.
Using the information in Exhibit 12.4, what Analytic Solver Platform function should be used in cell C10 to determine the number of Passengers to Board?

A) =PsiBinomial($C$8, 1-$C$6)
B) =PsiBinomial(1-$C$6, $C$8)
C) =PsiBinomial($C$8, $C$6)
D) =PsiBinomial($C$6, $C$8)

Question 49

A good way to fit the distribution to historical patterns when historical data is available is to

A) use the Fit icon in the Tools group of the Analytic Solver Platform
B) guess the distribution parameters
C) assume that the data distribution is Normal
D) assume that the data distribution is Weibull

Question 50

Large sample size, n, is desirable because

A) upper and lower limits of the confidence interval for the true population mean are closer to one another
B) upper and lower limits of the confidence interval for the true population mean are further apart
C) point estimate of the population mean is larger
D) point estimate of the population mean is smaller

Question 51

If a spreadsheet simulation user has a probability distribution that may assume 1 of 5 values with nearly equal probability, this user has what type of distribution?

A) A discrete distribution.
B) A continuous distribution.
C) A triangular distribution.
D) A normal distribution.

Question 52

Which of the following do not help determine the magnitude of risk in a decision-making problem?

A) The level of uncertainty in outcome.
B) The magnitude of potential loss.
C) The level of management interest in the problem.
D) The level of uncertainty in input variables.

Question 53

Exhibit 12.2
The following questions use the information below.
The owner of Fix-a-dent Auto Repair wants to study the growth of his business using simulation. He is interested in simulating the number of damaged cars and the amount of damage to the cars each month. He currently repairs 100 cars per month and feels the change in number of cars can vary uniformly between a decrease of as much as 3% and an increase of up to 5% (average change of 1%). The dollar value of the damage to the cars is a normally distributed random variable with a mean of $3,000 and a standard deviation of $500. The average repair bill has been increasing steadily over the years and the owner expects the mean repair bill will increase by 1% per month. A spreadsheet model to simulate the problem has been run 300 times. A part of the simulation statistics output from Risk Solver Platform (RSP)and a spreadsheet for computing confidence intervals follows.
Using the information in Exhibit 12.2, what formula should go in cell B8 of the Confidence Intervals spreadsheet to compute the upper limit on a 95% confidence interval for the true population mean?

A) =B4+1.96*B5/SQRT(B2)
B) =B4+1.645*B5/SQRT(B2)
C) =B4-1.96*B5/SQRT(B2)
D) =B4+1.96*B5/B2

Question 54

What method is used to generate observations from a distribution?

A) random number generator
B) sample generator
C) problem generator
D) steady state generator

Question 55

Exhibit 12.1
The following questions use the information below.
The owner of Fix-a-dent Auto Repair wants to study the growth of his business using simulation. He is interested in simulating the number of damaged cars and the amount of damage to the cars each month. He currently repairs 100 cars per month and feels this can vary uniformly between a decrease of as much as 3% and an increase of up to 5% (average change of 1%) over the previous months. The dollar value of the damage to the cars is a normally distributed random variable with a mean of $3,000 and a standard deviation of $500. The average repair bill has been increasing steadily over the years and the owner expects the mean repair bill will increase by 1% per month. You have created the following spreadsheet to simulate the problem.
Using the information in Exhibit 12.1, what Analytic Solver Platform function should go in cell B9 and copied to B10:B19 to compute the number of cars repaired in the subsequent months?

A) =PsiUniform($B$8*(1+$F$2), $B$8*(1-$H$2))
B) =PsiUniform(B8*(1-$F$2), B8*(1+$H$2))
C) =PsiUniform($C$2*(1-$F$2), $C$2*(1+$H$2))
D) =PsiIntUniform($C$2*(1-$F$2), $C$2*(1+$H$2))

Question 56

Exhibit 12.4.
The following questions use the information below.
The manager of a Washington, DC sightseeing tour company is concerned about overbooking for one of his bus tours. The bus has 15 seats but sometimes there are empty seats. His records show that about 20% of ticket holders do not show up for their tour. Tickets cost $10 and are non-refundable. If the manager overbooks the tour and more than 15 passengers show up, some of them will be bumped to a later tour. This bumping costs the company $25 in various expenses to keep the customer happy until the next tour. The manager wants to see what happens to profits if 18 reservations are accepted.
Using the information in Exhibit 12.4, what formula should go in cell C15 of the worksheet to determine the Marginal Profit?

A) =C12+C13+C14
B) =C12-C13-C14
C) =C12-C14+C13
D) =C12-(C13-C14)

Question 57

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Using the information in Exhibit 12.3, what formula should go in cell H3 to compute the service level?

A) =SUM(G8:G21)/SUM(D8:D21)
B) =SUM(D8:D21)/SUM(E8:E21)
C) =SUM(E8:E21)/SUM(D8:D21)
D) =SUM(F8:F21)/SUM(G8:G21)

Question 58

Inventory position is defined as

A) ending inventory + outstanding orders
B) ending inventory − backorders
C) outstanding orders − on hand inventory
D) ending inventory

Question 59

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Using the information in Exhibit 12.3, what Analytic Solver Platform function should be used for generating a random shipping time based on the Data spreadsheet distribution for shipping time?

A) =PsiCumul($B$6:$C$8)
B) =PsiCustom($B$6:$B$8, $C$8:$C$8)
C) =PsiGeneral(Data!$B$6, probability $C$8)
D) =PsiDiscrete($B$6:$B$8, $C$8:$C$8)

Question 60

The worst-case analysis approach to risk analysis

A) is optimistic
B) is pessimistic
C) is most likely
D) generally produces good outcomes

Question 61

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
A variable whose value cannot be predicted or set with certainty is a

A) discrete variable
B) random variable
C) realistic variable
D) simulation variable
Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

Question 62

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
A simulation model was replicated 100 times yielding a mean of 82.59 with variance of 17.66. Of the 100 replications, 11 replications yielded an outcome over a value of 100. The 95% confidence interval of the mean is the interval (81.77, 83.41). Of the 100 simulation outcomes, 65 outcomes failed to fall within this interval. What is wrong with the confidence interval?

Question 63

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The spreadsheet model for Sal, from Exhibit 12.5, has been run 300 times to produce the following output. What is the best case scenario for Sal based on this output? Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

Question 64

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
Sal, from Exhibit 12.5, has produced the following spreadsheet to compute confidence intervals on his income. What formula should go in cell B12 to compute the upper limit on a 95% confidence interval for the population proportion below 90%? Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

Question 65

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What function should be used for generating random numbers from a normal distribution with mean μ and standard deviation σ?

Question 66

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
A machine produces an average of 500 parts per day with a standard deviation of 10 parts. This is a normally distributed variable. The percent of defective parts ranges from 8-12%. Parts which need minor repair comprise 75% of the defective parts and cost $5 to repair. The rest of the defective parts cost $20 to repair. What formulas should go in cells B8:B15 to compute the daily cost of defective parts? Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

Question 67

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What function should be used for generating random integer numbers between 2 and 8?

Question 68

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What function should be used for generating random numbers from a normal distribution with mean μ and standard deviation σ between the values of a and b only?

Question 69

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Jim Johnson operates a bus service to take college students to "The Big City" on Friday night and bring them back to school on Sunday night. The bus has 45 seats but sometimes there are empty seats. His records show that about 5% of ticket holders do not show up for their ride. Tickets cost $20 and are non-refundable. If Jim overbooks the bus and more than 45 passengers show up, some of them will be bumped and have to miss the trip. This bumping costs the company $40 because Jim has a double-your-money back policy for bumped passengers. Jim wants to see what happens to profits if 48 reservations are accepted. What formulas should go in cell C10 − C15 of the worksheet?

Question 70

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What is the expected number of phone calls per hour based on the following distribution on the number of phone calls per hour?

Question 71

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Why would a manager be interested in analyzing risk?

A) To determine a most likely outcome.
B) To determine a range of outcomes.
C) To determine a distribution of outcomes.
D) To determine a confidence interval on most likely outcomes.

Question 72

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
A simulation model was replicated 100 times yielding a mean of 82.59 with variance of 17.66. Of the 100 replications, 11 replications yielded an outcome over a value of 100. What is the 95% confidence interval on the proportion of simulations whose outcomes exceeded a value of 100?

Question 73

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
University Florists makes bouquets from a variety of materials. The Daily Special Bouquet is priced at $20. The florist assembles this bouquet each day from a variety of low cost flowers he buys from his flower supplier. The actual cost of flowers ranges uniformly from $2 to $7, with all intermediate values being equally likely. The florist (who studied management science many years ago) knows that the time to assemble a bouquet is normally distributed with a mean time of 5 minutes and standard deviation of 1 minute. This will be the time required for all of the Daily Special Bouquets for that day. The florist values his labor time at $10 per hour. Sales are normally distributed with a mean of 10 bouquets per day with a standard deviation of 1 bouquet. What formulas should go in cells B8:B14 to simulate daily profits for the store? Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

Question 74

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What function should be used for generating random numbers from the following distribution on the number of phone calls per hour?

Question 75

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
A simulation model was replicated 100 times yielding a mean of 82.59 with variance of 17.66. Of the 100 replications, 11 replications yielded an outcome over a value of 100. What is the 90% confidence interval on the mean?
Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

Question 76

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What is the probability that 3 or more phone calls are received in any hour of operation? Instructions: Answer the following questions using the Analytic Solver Platform Excel add-in.

Question 77

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
Sal, from Exhibit 12.5, has produced the following spreadsheet to compute confidence intervals on his income. What formula should go in cell B8 to compute the upper limit on a 95% confidence interval for the true population mean?

Question 78

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What gallery distribution should be used for generating the number of times "tails" come up over 15 flips of a "fair" coin?

Question 79

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Using the information in Exhibit 12.3, what formula should go in cell J8 to determine the arrival date for an order?

A) =IF(I8=0,0,A8+I8)
B) =IF(I8=0,0,A8+1+I8)
C) =IF(I8=1,0,A8+1+I8)
D) =IF(I8=0,A8+1+I8,0)

Question 80

Exhibit 12.3
The following questions use the information below.
An auto parts store wants to simulate its inventory system for engine oil. The company has collected data on the shipping time for oil and the daily demand for cases of oil. A case of oil generates a $10 profit. Customers can buy oil at any auto parts store so there are no backorders (the company loses the sale and profit). The company orders 30 cases whenever the inventory position falls below the reorder point of 15 cases. Orders are placed at the beginning of the day and delivered at the beginning of the day so the oil is available on the arrival day. An average service level of 99% is desired. The following spreadsheets have been developed for this problem. The company has simulated 2 weeks of operation for their inventory system. The current level of on-hand inventory is 25 units and no orders are pending.
Using the information in Exhibit 12.3, what formula should go in cell G9 to compute inventory position?

A) =G8+E9-IF(H8=1,$D$4,0)
B) =G8-E9+IF(H8=1,$D$4,0)
C) =G8-E9+IF(H8=1,$D$5,0)
D) =G8-E9+IF(H8=1,0,$D$4)