Deck 12: Introduction to Simulation Using Risk Solver Platform

Question 1

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).

Answer 1

D

Question 2

What is the correct Risk Solver Platform (RSP) function for generating random numbers from the following distribution on the number of children in families (assume a reference to the current worksheet). $$\begin{array} { c c c } & \text { A } & \text { B } \\1 & \# \text { of children } & \text { P(\# af children) } \\ 2 & 1 & 0 .20 \\3 & 2 & 0.30 \\4 & 3 & 0.25 \\5 & 4 & 0.20 \\6 & 5 & 0.05\end{array}$$

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

Answer 2

=PsiDiscrete(A2:A6,B2:B6)

Question 3

What method is used to generate observations from a distribution?

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

Answer 3

A

Question 4

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 5

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 6

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 7

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 8

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

Question 9

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 10

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

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

Question 11

Which Risk Solver Platform (RSP) 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 12

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

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

Question 13

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 Risk Solver Platform (RSP) 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 14

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 Risk Solver Platform (RSP) 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 15

Which Risk Solver Platform (RSP) 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 16

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 17

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

A) Use the Risk Solver Platform (RSP)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 Risk Solver Platform (RSP) distribution fitting tools.
D) The distributions selected should represent the underlying pool of values expected to occur.

Question 18

The Risk Solver Platform (RSP) 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 19

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 Risk Solver Platform (RSP) 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 20

Which of the following distributions can be generated by Risk Solver Platform (RSP)?

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

Question 21

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 22

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 23

Inventory position is defined as

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

Question 24

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 25

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 26

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 27

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 28

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 Risk Solver Platform (RSP) 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 29

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 Risk Solver Platform (RSP) 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 30

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.
$\begin{array}{|l|l|}\hline {\text { Simulation Statistics }} \\\hline \text { Name } & \text { Income/Revenue } \\\hline \text { Description } & \text { Output } \\\hline \text { Cell } & \text { D21 } \\\hline \text { Minimum= } & 3339249.82 \\\hline \text { Maximum= } & 5086714.77 \\\hline \text { Mean= } & 4119518.91 \\\hline \text { Std Deviation= } & 291116.83\\\hline\end{array}$


-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 31

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 32

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.
$\begin{array}{|l|l|}\hline {\text { Simulation Statistics }} \\\hline \text { Name } & \text { Income/Revenue } \\\hline \text { Description } & \text { Output } \\\hline \text { Cell } & \text { D21 } \\\hline \text { Minimum= } & 3339249.82 \\\hline \text { Maximum= } & 5086714.77 \\\hline \text { Mean= } & 4119518.91 \\\hline \text { Std Deviation= } & 291116.83\\\hline\end{array}$


-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

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

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 35

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 36

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 37

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.
$\begin{array}{|l|l|}\hline {\text { Simulation Statistics }} \\\hline \text { Name } & \text { Income/Revenue } \\\hline \text { Description } & \text { Output } \\\hline \text { Cell } & \text { D21 } \\\hline \text { Minimum= } & 3339249.82 \\\hline \text { Maximum= } & 5086714.77 \\\hline \text { Mean= } & 4119518.91 \\\hline \text { Std Deviation= } & 291116.83\\\hline\end{array}$


-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 38

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)

Question 39

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 Risk Solver Platform (RSP) 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 40

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 Risk Solver Platform (RSP) 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 41

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 42

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

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

Question 43

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.

Using the information in Exhibit 12.5 and the Risk Solver Platform (RSP), what formulas should go in cells B8:D21 of the spreadsheet?

Question 44

An office supply store wants to simulate its inventory system for notebooks. The company has collected data on the shipping time and daily demand for notebooks. Each notebook generates a $2 profit. Customers can buy notebooks at any office supply store so there are no backorders (the company loses the sale and profit). The company orders 200 notebooks whenever the inventory position falls below the reorder point of 100 notebooks. Orders are placed at the beginning of the day and delivered at the beginning of the day so the notebooks are available on the arrival day. The average daily demand is 23.5 notebooks. An average service level of 99% is desired. There are currently 25 notebooks on hand and no orders are pending. The following spreadsheets have been developed for this problem. The company has simulated 1 month of operation for its inventory system. (HINT: This covers Rows 8 to 37 of the spreadsheet.) What formulas go in cells A1:J37 of the "Model" worksheet for this simulation?

Question 45

What function should be used for generating random integer numbers between 2 and 8?

Question 46

What function should be used for generating random numbers between a and b from a symmetric triangular distribution when the most likely value is (a + b)/2?

Question 47

What function should be used for generating random numbers from the following distribution on the number of phone calls per hour?

Question 48

What function should be used for generating random numbers from a normal distribution with mean  and standard deviation  between the values of a and b only?

Question 49

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 50

What function should be used for generating random numbers from a normal distribution with mean  and standard deviation ?

Question 51

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 52

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 53

What function should be used for generating random numbers between 1 and 12 from a continuous uniform distribution?

Question 54

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?

Question 55

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?

Question 56

What is the probability that 3 or more phone calls are received in any hour of operation?

Question 57

What gallery distribution should be used for generating the number of times "tails" come up over 15 flips of a "fair" coin?

Question 58

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%?

Question 59

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

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

Question 60

What is the expected number of phone calls per hour based on the following distribution on the number of phone calls per hour?

Question 61

Project 12.1- Monte Carlo Integration
A common application of Monte Carlo simulation is to provide numerical approximations. One such application is to approximate the area under a curve, or Monte Carlo integration. The following figure represents such a curve, defined over the range of X = 0 to X = 13. Call the area under this curve A.
Monte Carlo integration begins by overlaying on the curve of interest a region (call this region, B) whose area is easy to calculate (i.e., a box). Monte Carlo integration then involves the random generation of points in B and a determination of the percentage of these points that fall in A (i.e., fall below the curve). This percentage represents that portion of the area of B that is the area of A.
Use Monte Carlo integration techniques to approximate the area under the curve. Use exact techniques to calculate the true area under the curve. How accurate is your approximation?

Question 62

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 plans to accept 48 reservations (overbook 3 seats).
What is Jim Johnson's expected marginal profit?

Question 63

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?

Question 64

Project 12.2  Friendly Bank Services
Friendly Bank has various branches throughout the city. Ronnie Fare is a branch manager. Ronnie has always been very customer focused. Her branch is relatively small; three counter tellers and two drive-through tellers. Her drive-through support appears more than adequate. Her concern is with the in-branch service. She is concerned with the level of service being provided and whether or not each of her three tellers are of equal proficiency.
When a customer comes in for service, they wait in a single line and move to the first available teller. Once serviced, the customer leaves the bank. Six weeks ago, Ronnie enlisted a small company to conduct time studies of the bank processes. The data was collected over a four-week period. This extended collection period helped overcome bias in the data collection due to observation activities. The final set of data just arrived in the mail and Ronnie is ready to conduct some desk-top analysis of the data to answer her own questions about her branch.
The data pertinent to her concerns are:
At first glance, it appears there is no difference between the tellers. However, Ronnie wants to simulate the bank process to provide estimates on the following pieces of information:
Build a simulation model to help answer Ronnie Fare's questions. Use 250 arrivals per day. Provide appropriate statistical information in your answer.

Question 65

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?