Jiminy Sweeps is the owner of Ash Kickers, Inc. a chimney cleaning business. Jiminy has just bought an expensive chimney cleaning machine. The machine uses special brushes that only fit this machine. Jiminy is uncertain how many sets of these brushes he will need during the useful life of the machine. The probability distribution for the number of brush sets needed during the life of the machine is given by the following: Brush Sets Needed Probability 20 .2 30 .6 40 .2 If Jiminy buys the brush sets as part of the machine purchase, the cost is $300 per set. If Jiminy buys them later as he needs them, the cost jumps to $500 per set. If Jiminy buys too many sets with the machine purchase and doesn’t need them, their salvage value is only $100 per set a. Draw the Payoff Table and the Opportunity Loss tables. b.Find the optimal action according to Maximax, Maximin, and Maximum Likelihood. c. Write the expressions for the EMVs. d. If the optimal EMV has a value of -$9,800, write the expression for EVPI.

Jiminy Sweeps is the owner of Ash Kickers, Inc. a chimney cleaning business. Jiminy has just bought an expensive chimney cleaning machine. The machine uses special brushes that only fit this machine. Jiminy is uncertain how many sets of these brushes he will need during the useful life of the machine. The probability distribution for the number of brush sets needed during the life of the machine is given by the following: Brush Sets Needed Probability 20 .2 30 .6 40 .2 If Jiminy buys the brush sets as part of the machine purchase, the cost is $300 per set. If Jiminy buys them later as he needs them, the cost jumps to $500 per set. If Jiminy buys too many sets with the machine purchase and doesn’t need them, their salvage value is only $100 per set a. Draw the Payoff Table and the Opportunity Loss tables. b.Find the optimal action according to Maximax, Maximin, and Maximum Likelihood. c. Write the expressions for the EMVs. d. If the optimal EMV has a value of -$9,800, write the expression for EVPI.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter10: Introduction To Simulation Modeling

Section: Chapter Questions

Problem 41P: At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 =...

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At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.
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A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000 Construct a decision tree to help the farmer make his decision. What should he do?
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