Exam 14: Monte Carlo Simulation

The Excel function __________ generates integer values between lower and upper bounds.

Analytic Solver Platform (ASP) cannot guarantee an optimal solution to a simulation optimization model because

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 Use the negative binomial distribution to approximate the average number of pairs of shoes that a customer has to buy before purchasing two pair with a discount of at least 50%.

A ___________ analysis involves considering alternative values for the random variables and computing the resulting value for the output.

A specialty hedge fund is considering the purchase of a Jackson Pollock painting. It estimates the value of the painting to be $185 million. In an auction, both the number of competing bids and the amount of the competing bids is uncertain. The hedge fund has maintained a file summarizing 10 recent art auctions that it believes are similar to the upcoming auction. It is considering a bid of $163 million and would like to evaluate its chances of winning the upcoming auction with this bid. Bid Amount (As Fraction of Estimated Share Value) Company 1 0.817 0.884 0.756 2 0.771 0.863 0.825 0.819 0.851 0.786 3 0.804 0.851 0.786 0.851 4 0.880 0.756 0.874 0.877 0.910 5 0.890 0.804 0.819 0.860 0.880 0.880 6 0.851 0.786 0.896 0.784 0.792 0.792 7 0.881 0.786 0.804 0.819 8 0.804 0.819 0.860 0.880 0.773 0.824 9 0.819 0.896 0.877 0.860 0.784 0.819 0.880 10 0.756 0.804 0.786 0.786 0.819 0.885 a. Construct a spreadsheet simulation model to determine the likelihood of the hedge fund winning the auction. Use a discrete uniform distribution between the minimum and maximum number of bidders in the 10 observed auctions to model the number of bidders in the Jackson Pollock auction. Fit a realistic distribution to the bid data to generate values of competing bid amounts. b. For a bid amount of $163 million, estimate the probability of the hedge fund winning the auction?

A(n) ___________ is an input to a simulation model whose value is uncertain and described by a probability distribution.

A company has improved its anti-virus program and has released a new version. Assume there is a 0.6 probability that the users of this anti-virus will upgrade the version in any particular year. That is, the upgrade year of the user is a geometric random variable. The revenue generated from the upgrade (when it occurs) follows a normal distribution with a mean of $80,000 and a standard deviation of $22,000. a. Complete a simulation model that analyzes the net present value of the revenue from the user upgrade. Use an annual discount rate of 8 percent. b. What is the average net present value earned by the company? c. What is the standard deviation of net present value?

In a ___________, a random variable can take any value in a specified range.

A specialty hedge fund is considering the purchase of a Jackson Pollock painting. It estimates the value of the painting to be $185 million. In an auction, both the number of competing bids and the amount of the competing bids is uncertain. The hedge fund has maintained a file summarizing 10 recent art auctions that it believes are similar to the upcoming auction. It is considering a bid of $163 million and would like to evaluate its chances of winning the upcoming auction with this bid. Bid Amount (As Fraction of Estimated Share Value) Company 1 0.817 0.884 0.756 2 0.771 0.863 0.825 0.819 0.851 0.786 3 0.804 0.851 0.786 0.851 4 0.880 0.756 0.874 0.877 0.910 5 0.890 0.804 0.819 0.860 0.880 0.880 6 0.851 0.786 0.896 0.784 0.792 0.792 7 0.881 0.786 0.804 0.819 8 0.804 0.819 0.860 0.880 0.773 0.824 9 0.819 0.896 0.877 0.860 0.784 0.819 0.880 10 0.756 0.804 0.786 0.786 0.819 0.885 a. Construct a spreadsheet simulation model for this auction. Use a discrete uniform distribution between the minimum and maximum number of bidders in the 10 observed auctions to model the number of bidders in the Jackson Pollock auction. Fit a realistic distribution to the bid data to generate values of competing bid amounts. Use ASP to apply simulation optimization to determine the hedge fund's bid amount that maximizes the expected return = P(winning auction)*(185 - bid amount). Hint: Placing reasonable bounds on the highest and lowest possible bid amount will greatly assist the optimization algorithm. b. What is the probability that the hedge fund wins the auction if it bids the amount that maximizes its expected return?

Which of the following is true of verification?

The weekly demand for an item in a retail store follows a uniform distribution over the range 70 to 83. What would be the weekly demand if its corresponding computer-generated value is 0.5?

The range of computer-generated random numbers is

Consider the table below with information regarding each activity, immediate predecessors, and duration estimates (in minutes) for each activity. Activity Immediate Predecessors Minimum Time Likely Time Maximum Time A - 6 7 9 B - 4 9 11 C A 3 9 12 D B 2 6 12 E B, C 3 5 10 F D 4 7 9 G E 4 7 15 a. Using the PERT distribution in ASP to represent the duration of each activity, construct a simulation model to compute the total time to complete the task. b. What is the expected duration of the entire project? What is the standard deviation of the project duration? c. What is the likelihood that the project will be complete in 26 minutes?

A toy company designs a new toy car this season. The fixed cost to produce the car is $120,000. The variable cost which includes raw materials, production, and shipping costs, is $40 per car. The company will sell the car for $48 each. A distributor has agreed to pay the toy company $12 for each car remaining after the retail selling season. Forecasts are for expected sales of 55,000 toy cars with a standard deviation of 9000. The normal probability distribution is assumed to be a good description of the demand. The management has tentatively decided to produce 55,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision. ​ a. Create a what-if spreadsheet model using formula that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit corresponding to average demand (55,000 units)? b. Modeling demand as a normal random variable with a mean of 55,000 and a standard deviation of 9000, simulate the sales of the toy car using a production quantity of 55,000 units. What is the estimate of the average profit associated with the production quantity of 55,000 cars? How does this compare to the profit corresponding to the average demand (as computed in part a)? c. Before making a final decision on the production quantity, management wants an analysis of a more aggressive 65,000-unit production quantity and a more conservative 45,000-unit production quantity. Run your simulation with these two production quantities. What is the mean profit associated with each?

Which of the following inferences about a variable of interest can be drawn from the graph given below?

A distribution of a random variable for which values extremely larger or smaller than the mean are increasingly unlikely can possibly be modeled as a(n) _____________ probability distribution.

In reviewing the graph below, which of the following inferences can be drawn about the monthly salary?

____________ is the process of determining that a simulation model provides an accurate representation of a real system.

The values for random variables in a Monte Carlo simulation are

In a simulation process, the error of the estimates of the output can be reduced by