Scenario Analysis & Discussion Question

QSO 510 Module Ten 1

Module Nine explored sources of process variation and the use of control charts to eliminate unusual sources of variation to ensure that an operations process is “on control.” Module Ten introduces decision making under uncertainty and risk along with payoff tables and decision trees as vehicles to facilitate decision making. In making decisions, one considers alternative courses of action, states of nature that are naturally occurring events not controlled by the decision maker, and the potential payoffs (usually monetary rewards, sometimes costs) from each course of action. For example, a new college graduate may consider two alternative courses of action: a job offer in Houston, Texas, and a job offer in New York City. She may encounter two states of nature: a low cost of living (COL) and a high cost of living. The payoffs, the monetary values of the job offers in each city considering the COL, are shown in the payoff table below.

States of Nature

Actions Low COL High COL

Job Offer Houston $80,000 95,000

Job Offer New York City

74,000 140,000

The decision maker may face conditions of uncertainty or risk in making her decision. Under uncertainty, insufficient information exists to assign probabilities to the state of nature. A decision is made based on the decision maker’s optimism or pessimism about the cost of living. The pessimist will use the maximin strategy to make a decision. The optimist will make a decision using the maximax strategy. Using the maximax strategy, the maximum payoff from each alternative course of action is chosen and the maximum of those maximums is selected. Based on the table above, the maximum payoff from the Houston job offer is $95,000 and the maximum payoff from the New York City offer is $140,000. The maximum of those two payoffs is $140,000. The decision maker should select New York City with a potential payoff of $140,000. Using the maximin strategy of the pessimist, the minimum payoff from each alternative course of action is chosen and the maximum of those minimums is selected. Using the table above, the minimum payoff from the Houston job offer is $80,000 and the minimum payoff from the New York City offer is $74.000. The maximum of those two payoffs is $80,000. The decision maker should select Houston with a potential payoff of $80,000.

2 QSO 510 Module Ten

Under risk, either historical probabilities or subjective probabilities can be assigned to the state of nature. Using the prior year’s COL published indices, the probability of a low COL is 0.4 and the probability of a high COL is 0.6. Using the expected value (EV) criterion and applying these probabilities provides the following results:

EV(Houston) = 0.4(80,000) + 0.6(95,000) = $89,000 EV(NYC) = 0.4(74,000) + 0.6(140,000) = $113,600

The decision maker should select the New York City offer with an expected value of $113,600. Consider some additional examples of decision making. An oil pump manufacturer has to make a decision to purchase pistons used in the pumps or manufacture them in the company’s machine shop. The decision will be made given two states of nature, sales are low or sales are high for the oil pumps with potential profits from each option. A sales manager who travels to a nearby city for business must decide to travel by train or by plane. The final decision considers the cost of each option and two states of nature, inclement weather or good weather on that day.