Question

A manager is trying to decide whether to build a small, medium, or large facility. Demand can be low, average, or high, with the estimated probabilities being 0.25, 0.40, and 0.35, respectively.

A small facility is expected to earn an after-tax net present value of just $18,000 if demand is low. If demand is average, the small facility is expected to earn $75,000; it can be increased to medium size to earn a net present value of $60,000. If demand is high, the small facility is expected to earn $75,000 and can be expanded to medium size to earn $60,000 or to large size to earn $125,000.

A medium-sized facility is expected to lose an estimated $25,000 if demand is low and earn $140,000 if demand is average. If demand is high, the medium-sized facility is expected to earn a net present value of $150,000; it can be expanded to a large size for a net payoff of $145,000.

If a large facility is built and demand is high, earnings are expected to be $220,000. If demand is average for the large facility, the present value is expected to be $125,000; if demand is low, the facility is expected to lost $60,000.

Which alternative is best, according to each of the following decision criterion?

a) Maximin

b) Maximax

c) Minimax regret

Answer 1

Only the initial decision is made now. Subsequent decisions are made after it is known about the level of demand. Hence, for decision criterion, only initial decisions are considered.

We tabulate the given data in excel as shown below:

We find the best alternative using Maximin and Maximax criterion as shown below:

The above table in the form of formulas is shown below for better understanding and reference:

For minimax regret, we prepare a regret table as shown below:

Based on above, we find the best decision as shown below:

The above table in the form of formulas is shown below for better understanding and reference:

Hence, the best alternative as per below criterion is as shown below:

a) Maximin - Small facility

b) Maximax - Medium Facility

c) Minimax regret - Medium Facility

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