Exam 14: Monte Carlo Simulation

A distributor has generated a rough estimate of aftershave demand at their retails store. The distributor is confident that demand will range from 100 to 650. The following table lists weights for demand values within this range. ​ Demand 230 330 430 530 Weight 0.15 0.25 0.35 0.25 ​ The distributor pays a wholesale price of $21 per aftershave and then sells at a retail price of $31. ​ a. Construct a spreadsheet model that computes net profit corresponding to a given level of demand and specified order quantity. Model demand as a random variable with ASP's custom general distribution. b. Using simulation optimization, determine the order quantity that maximizes expected profit. What is the probability of running out of aftershave at this order quantity? c. How many aftershaves does the distributor need to order so that the probability of running out of aftershaves is only 25 percent? How much expected profit will the distributor lose if he orders this amount rather than the amount from part b?

In simulation analysis, the ___________ of random variables can be adjusted to determine the impact of the assumptions about the shape of the uncertainty on the results.

A description of the range and relative likelihood of possible values of an uncertain variable is known as a

___________ is a measure of dependence between two random variables.

A tourist bus can accommodate 80 people and currently books up to 80 reservations. Past data shows that the tourist bus always accommodates all 80 reservations but that, on average, two people do not show up. To capture additional profit, the travel agent is considering an overbooking strategy in which he would accept 82 reservations even though the tourist bus can accommodate only 80 people. The travel agent believes that he will be able to always book all 82 reservations. The probability distribution for the number of people showing up when 82 reservations are accepted is estimated as follows: ​ People Showing Up Probability 78 0.05 79 0.3 80 0.5 81 0.1 82 0.05 ​ The travel agent receives a marginal profit of $110 for each passenger who books a reservation (regardless whether they show up). The travel agent will also incur a cost for any passenger denied seating on the bus. This cost covers added expenses of rescheduling the passenger as well as loss of goodwill, estimated to be $160 per passenger. Develop a spreadsheet simulation model for this overbooking system. Simulate the number of passengers showing up. ​ a. What is the average net profit for each tourist bus with the overbooking strategy? b. What is the probability that the net profit with the overbooking strategy will be less than the net profit without overbooking (80 × $110 = $8,800)? c. Explain how your simulation model could be used to evaluate other overbooking levels such as 81, 83, and 84 and for recommending a best overbooking strategy.

A simulation model extends spreadsheet modeling by

In a(n) ___________ relationship between two quantities, either one quantity never increases as the other increases, or one quantity never decreases as the other increases.

Sunseel Industries produces different types of raw materials and it is interested in using simulation to estimate the profit per unit for its new product X. The selling price for the product will be $40 per unit. Probability distributions for the raw material cost, the production cost, and the marketing cost are estimated as follows. Raw Material Cost (\ ) Probability Production Cost (\ ) Probability Marketing Cost (\ ) Probability 16 0.20 10 0.25 5 0.40 18 0.30 11 0.45 6 0.60 20 0.35 12 0.30 22 0.15 ​ a. Compute profit per unit for the base case, worst case, and best case. b. Construct a simulation model to estimate the mean profit per unit. c. Management believes the project may not be sustainable if the profit per unit is less than $2. Use simulation to estimate the probability the profit per unit will be less than $2.

The Excel add-in __________ is used to design a spreadsheet simulation model.

Which of the following is true of simulation optimization using Analytic Solver Platform (ASP)?

A ___________ uses repeated random sampling to represent uncertainty in a model representing a real system and that computes the values of model outputs.

Team X is scheduled to play against Team Y in an upcoming game in Baseball's World Series. Assume that each player's point production can be represented as an integer uniform variable with the ranges provided in the following table: ​ Player Team X Team Y 1 [4,10] [2,4] 2 [2,6] [14,30] 3 [7,20] [2,20] 4 [3,5] [1,10] 5 [6,20] [8,20] 6 [5,10] [7,12] 7 [7,10] [14,20] 8 [12,40] [3,5] 9 [9,20] [14,25] ​ a. Develop a spreadsheet model that simulates the points scored by each team. b. What are the average and standard deviation of points scored by Team X? What is the shape of the distribution of points scored by Team X? c. What are the average and standard deviation of points scored by Team Y? What is the shape of the distribution of points scored by Team Y? d. Let Point Differential = Team X points - Team Y points. What is the average point differential between the two teams? What is the standard deviation in the point differential? What is the shape of the point differential distribution? e. What is the probability that the Team X scores more points than the Team Y?

A store is offering a discount on 800 pairs of basketball shoes. The amount of the discount varies and is not revealed to the customer until checkout. The distribution of discounts is given in the below table. Discount Rate (\%) Number of Tags 5 250 20 220 35 120 50 80 65 70 90 60 How many pairs of shoes does a customer have to buy so that, on average, he has purchased five containing a 65% or 90% discount? (Hint: Use the hypergeometric distribution in ASP to answer this question.)

In Excel, the expression LN(RAND())*(-m) would generate a(n) __________ random variable with mean m.

An input to a simulation model that is selected by the decision maker is known as a

The __________ function is used to generate a pseudorandom number in Excel.

A company has produced a new battery with an estimated mean lifetime of 60 hours. Management also believes that the standard deviation is 4.5 hours and that battery hours are normally distributed. To promote the new battery, management has offered to refund some money if the battery fails to reach 50 hours before the battery needs to be recharged. Specifically, for batteries with a lifetime below 50 hours, the management will refund a customer $50 per hour short of 50 hours. a. For each battery sold, what is the expected cost of the promotion? b. What hours should the company set the promotion claim if it wants the expected cost to be $0.50?

The choice of the probability distribution for a random variable can be guided by

Which of the following is a disadvantage of using simulation?