Question

Us the case below to answer the following question(s).

MJ Logistics has decided to build a new warehouse to support its supply chain activities. They have the option of building either a large warehouse or a small one. Construction costs for the large facility are R8 million versus R5 million for the small facility. The profit (excluding construction cost) depends on the volume of work the company expects to contract for in the future. This is summarized in the table below (in millions of rand):

	High Volume	Low Volume
Large Warehouse	R35	R20
Small Warehouse	R15	R9

The company believes that there is a 60% chance that the volume of demand will be high.

a) Construct a decision tree to identify the best choice.

b) Suppose that the company engages some economic experts to provide their opinion about the future economic conditions. Historically, their upside predictions have been 75% accurate, while their downside predictions have been 90% accurate. Determine the best strategy if their predictions suggest that the economy will improve or will deteriorate. What is the expected value of sample information (EVSI) and what is expected value of perfect information (EVPI)?

Answer 1

a)

Decision tree is following:

EMV of Large warehouse = 0.6*35+0.4*20-8 = R 21 million

EMV of Small warehouse = 0.6*15+0.4*9-5 = R 7.6 million

EMV of Large warehouse is higher. Therefore, best choice is Large warehouse

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b)

Decision tree including the alternative of engaging with market expert, is following:

If prediction suggests that economy will improve, then

EMV of Large warehouse = 0.918*35+0.082*20-8 = 25.78 m

EMV of Small warehouse = 0.918*15+0.082*9-5 = 9.51 m

EMV of Large warehouse is higher. Therefore, in this case, best strategy is to build a Large warehouse

.

If prediction suggests that economy will deteriorate, then

EMV of Large warehouse = 0.2941*35+0.7059*20-8 = 16.41 m

EMV of Small warehouse = 0.2941*15+0.7059*9-5 = 5.76 m

EMV of Large warehouse is higher. Therefore, in this case, best strategy is to build a Large warehouse

EMV of engaging with market expert = 0.49*25.78+0.51*16.41 = 21 m

Max EMV without engaging with market expert = 21 m (as determined in part a)

EVSI = EMV of engaging with market expert - Max EMV without engaging with market expert

= 21 - 21

= 0

..

Expected Value with Perfect Information, EVwPI = 0.6*(35-8)+0.4*(20-8) = 21 m   (Payoff of large warehouse is higher in case of both high and low demand)

EVPI = EVwPI - EVw/oPI (EVw/oPI = Max EMV as determined in part a)

= 21 - 21

= 0