Question

Given is a decision payoff table.

		Future Demand
Alternatives	Low	Moderate	High
Small Facility	33	22	18
Medium Facility	19	32	22
Large Facility	-10	29	43

a) The best decision under uncertainty using MAXIMAX is to select  facility
  
b) The best decision under uncertainty using MAXIMIN is to select  facility
  
c) The best decision under uncertainty using LAPLACE/EQUALITY LIKELY is to select  facility

d) If the probabilities for Future Demand when it is Low = 0.35, Moderate = 0.30, and High = 0.35, the expected monetary value (EMV) for the large facility = .

e) If the probabilities for Future Demand when it is Low = 0.35, Moderate = 0.30, and High = 0.35, the best decision under risk is to select facility.

Answer 1

a)

Maximax - Find the maximum payoff for each alternative and select the alternative which gives the maximum of these maximums.

Alternatives	Future Demand			Max
	Low	Moderate	High	Payoff
Small Facility	33	22	18	33
Medium Facility	19	32	22	32
Large Facility	-10	29	43	43

So,

Best decision = Large facility

b)

Maximin - Find the minimum payoff for each alternative and select the alternative which gives the maximum of these minimums.

Alternatives	Future Demand			Min
	Low	Moderate	High	Payoff
Small Facility	33	22	18	18
Medium Facility	19	32	22	19
Large Facility	-10	29	43	-10

So,

Best decision = Small facility

c)

Laplace - Find the average payoff for each alternative and select the alternative which gives the maximum of these averages.

Alternatives	Future Demand			Average
	Low	Moderate	High	Payoff
Small Facility	33	22	18	24.33
Medium Facility	19	32	22	24.33
Large Facility	-10	29	43	20.67

So,

Best decision = Small or Medium facility

d)

The EMV for large facility = 0.35*(-10) + 0.30*(29) + 0.35*(43) = 20.25

e)

The EMV for large facility = 0.35*(-10) + 0.30*(29) + 0.35*(43) = 20.25
The EMV for medium facility = 0.35*(19) + 0.30*(32) + 0.35*(22) = 23.95
The EMV for small facility = 0.35*(33) + 0.30*(22) + 0.35*(18) = 24.45

So,

Best decision = Small facility