Question

A wheel alignment shop wants to improve his service by purchasing a new wheel alignment system. He is faced with three outcomes related to the demand on wheel alignment service, and three alternative decisions on alignment system purchase. The table below displays the estimated daily payoffs resulting from all combinations of decisions with outcomes.

Alternative Decisions Outcomes (demand)
O1: High O2: Moderate O3: low
A1: high performance alignment system AED 10,000 AED 5,000 AED -10,000
A2: ordinary alignment system AED 5,000 AED 3,000 AED -5,000
A3: no purchase AED 3,000 AED 2,000 AED 0
Probabilities 0.2 0.5 0.3

1. If the decision is taken under uncertainty, find the best decision using the Maximax criterion. (3.5 Marks)
2. Now with the given outcomes’ probabilities, what is the best decision according to the EMV criterion? (3.5 Marks)
3. Use the EVPI to decide if the shop manager should buy perfect information for AED 2500 or not.

Answer 1

We tabulate the given data in excel as shown below:

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

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

Hence, the best decision using the Maximax criterion is A1: High-Performance alignment system

We find EMV for each alternative as shown below:

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

As seen from above, the highest EMV is for A3: no purchase.

Hence, the best decision according to the EMV criterion is A3: No purchase

3) The maximum EMV is $1600 for A3: No purchase, which is the expected outcome without perfect information.

The best outcome for the state of nature “High” is A1: High Performance with a payoff of AED 10,000. The best outcome for the state of nature “Moderate” is A1: High Performance with a payoff of AED 5000. The best outcome for the state of nature “Low” is A3: No purchase with a payoff of AED 0.

Expected value with perfect information = (10,000)(0.2) + (5000)(0.5) + (0)(0.3) = 2000 + 2500 + 0 = AED 4500

Thus:
EVPI = EVwPI - Maximum EMV
= 4500 - 1600 = AED 2900

The expected value of perfect information = AED 2900

Hence, if perfect information is available for AED 2500 which is less than the Expected value of perfect information, the shop manager should buy it.

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