A manager is trying to decide whether to build a small, medium, or large facilit
ID: 393128 • Letter: A
Question
A manager is trying to decide whether to build a small, medium, or large facility. Demand can be lovw average, or high, with the estimated probabilities being 0.40, 0.35, and 0.25, respectively A small facility is expected to earn an after-tax net present value of just $14,000 if demand is low. If demand is average, the small facility is expected to earn $15,000; it can be increased to medium size to earn a net present value of $70,000. If demand is high, the small facility is expected to earn $25,000 and can be expanded to medium size to earn $80,000 or to large size to earn $155,000 A medium-sized facility is expected to lose an estimated $50,000 if demand is low and earn $90,000 if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of $100,000; it can be expanded to a large size for a net payoff of $115,000 If a large facility is built and demand is high, earnings are expected to be $160,000. If demand is average for the large facility, the present value is expected to be S80,000; if demand is low, the facility is expected to lose $70,000 Which alternative is best according to each of the following decision criterion? (Enter your responses as whole numbers.) Criterion a. Maximin b. Maximax c. Minimax regret Decision Value of Return $thousand thousand $thousand Enter vour answer in each of the answer boxesExplanation / Answer
Lets first create the payoff table as follows -
Now multiply the various above values with given respective probabilities (for eg. 14000*0.4 = 5600) to have the following figures –
Probability Small Facility Medium Facility Large Facility
Low 0.4 5600 -20000 -28,000
Average 0.35 5250 or 24500 31500 28,000
High 0.25 6250 or 20000 or 38750 25,000 or 28750 40,000
The Maximax criteria involves selecting the alternative that maximizes the maximum payoff available.
Look at the payoff table, the highest payoff is 40,000which is earned when large facility is established with expectation of high demand. Hence the large facility will be choosen with Maximax criteria.
The MAximin involves selecting the alternative that maximizes the minimum payoff acheivable. Now look at table, if small factory is choosen the minium payoff is 5600, if medium is choosen the minimum payoff is -50000 and with largest facility the minium payoff is -28000. Among all these minimum payoffs the maximum payoff is 5600. Hence the smallest facility will be choosen.
Minimax regret involves minimizing the maximum regret. Regret is the opportunity loss because of wring decision made. For example if the demand is low and we decided small facility the payoff is 14000 but if we had choosen medium we would incur -50000. That is if we had choosen the worng option of medium facility when demans is low our maximum regret is not only loosing 14000 but also incuring loss of 50000 hence total regret of 14000+50000 = 64000. Similarly when largest was choosen when the demand was low, the regret would be 14000+70000 = 84000.
Similarly the following table shows the regret values -
Now multiply with probabilities to get the following result -
Probability Small Facility Medium Facility Large Facility
Low 0.4 0 25600 33600
Average 0.35 26250 or 7000 0 3500
High 0.25 33750 or 20000 or 250 1250 or 15000 0
Now in the above regret table, the maximum regrets are -
when small facility is choosen it is 7000, when medium is choosen it is 25600 and when largest is choosen it is 33600. Amongs these the minium is 25600. Hence the medium facility will be choosen.
Thus,
DEMAND FACILITY Probability Small Facility Medium Facility Large Facility Low 0.4 14000 -50000 -70,000 Average 0.35 15000 or 70000 90000 80,000 High 0.25 25,000 or 80,000 or 155,000 100,000 or 115,000 160,000Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.