Chapter 5: Decision-making Concepts Quantitative Decision Making with Spreadsheet Applications 7th ed. By Lapin and Whisler Sec 5.5 : Other Decision Criteria Sec 5.6: Opportunity Loss and the Expected Value of Perfect Information

The Maximin Payoff Criterion The maximin payoff criterion is a procedure that guarantees that the decision maker can do no worse than achieve the best of the poorest outcomes.

Example: Tippi-Toes Payoff Table Event (level of demand) Act (choice of movement) Gears and Levers Spring Action Weights and Pulleys Light $25,000 -$10,000 -$125,000 Moderate $400,000 $440,000 Heavy $650,000 $740,000 $750,000

Example Goal: Ensure a favorable outcome no matter what happens. Determine the worst outcome for each act regardless of the event. Gears and Levers Light demand $25,000 Spring Action -$10,000 Weights and Pulleys -$125,000

Example Choose an act with the largest lowest payoff. This guarantees a minimum return that is the best of the poorest outcomes possible. Gears and Levers will guarantee the toy manufacturer a payoff of at least $25,000. Gears and Levers is the maximin payoff act.

Example: Tippi-Toes Payoff Table Event (level of demand) Act (choice of movement) Gears and Levers Spring Action Weights and Pulleys Light $25,000 -$10,000 -$125,000 Moderate $400,000 $440,000 Heavy $650,000 $740,000 $750,000 Column Minimums

Risk vs. Reward Event Act A1 A2 E1 $0 -$1 E2 1 10,000 Event Act B1 B2 Column Minimums Event Act B1 B2 E1 $1 $10,000 E2 -1 -10,000 Column Minimums -$1 -$10,000

Deficiencies of Maximin Payoff Criterion It is an extremely conservative decision criterion and may lead to some bad decisions. It is primarily suited to decision problems with unknown probabilities that cannot be reasonably assessed.

The Maximum Likelihood Criterion The maximum likelihood criterion focuses on the most likely event to the exclusion of all others.

Maximum Likelihood Act Event (level of demand) Probability Act (Choice of Movement) Gears & Levers Spring Action Weights & Pulleys Light .10 $25,000 -$10,000 -$125,000 Moderate .70 400,000 440,000 Heavy .20 650,000 740,000 750,000

Maximum Likelihood Criterion Ignores most of other possible outcomes. Prevalent decision-making behavior.

The Criterion of Insufficient Reason Used when decision maker has no information about the event probabilities. Assumes each event has a probability of 1/(number of events) of occuring. Some knowledge of the probability of an event is almost always available.

The Bayes Decision Rule The Bayes decision rule chooses the act maximizing expected payoff. It makes the greatest use of all available information. Its major deficiency occurs when alternatives involve different magnitudes of risk.

Event Probability Act C1 Act C2 Payoff Payoff x Prob E1 .5 E2 -$1,000,000 -$500,000 $250,000 $125,000 E2 2,000,000 1,000,000 750,000 375,000 Expected Payoff $500,000

Opportunity Loss Opportunity loss is the amount of payoff that is forgone by not selecting the act that has the greatest payoff for the event that actually occurs. To calculate opportunity losses the maximum payoff for each row is determined and it’s then subtracted from its respective row maximum.

(in thousands of dollars) Event (level of demand) Payoff Row Maximum Gears & Levers Spring Action Weights & Pulleys Light $25,000 -$10,000 -$125,000 Moderate 400,000 440,000 Heavy 650,000 740,000 750,000 Row maximum-Payoff = Opportunity Loss (in thousands of dollars) 25-25=0 25-(-10)=35 25-(-125)=150 440-400=40 440-440=0 750-650=100 750-740=10 750-750=0

Opportunity Loss Table Event (level of demand) Act (choice of movement) Gears & Levers Spring Action Weights & Pulleys Light $0 $35,000 150,000 Moderate 40,000 Heavy 100,000 10,000

The Bayes Decision Rule and Opportunity Loss The Bayes decision rule is to select the act that has the maximum expected payoff or the minimum expected opportunity loss.

Act (choice of movement) Event (level of demand) Probability Act (choice of movement) Gears & Levers Spring Action Weights & Pulleys Loss Loss x Prob Light .10 $0 $35,000 $3,500 $150,000 $15,000 Moderate .70 40,000 28,000 Heavy .20 100,000 20,000 10,000 2,000 Expected Opportunity Loss $48,000 $5,500 $43,000

The Expected Value of Perfect Information When the decision maker can acquire perfect information the decision will be made under certainty. Then the decision maker can guarantee the best decision. We want to investigate the worth of such information before it is obtained, so we will determine the expected payoff once perfect information is obtained. This quantity is called the expected payoff under certainty.

Calculating Expected Payoff Under Certainty Determine the highest payoff for each event. Multiply the maximum payoffs with their respective event probabilities. Then sum these amounts. Determine the worth of perfect information to the decision maker.

Example: Highest Payoff for each Event Event(level of demand) Probability Act Under Certainty Gears & Levers Spring Action Weights & Pulleys Maximum Payoff Chosen Act Payoff x Prob Light .10 $25,000 -$10,000 -$125,000 G&L $2,500 Moderate .70 400,000 440,000 SA 308,000 Heavy .20 650,000 740,000 750,000 W&P 150,000 Expected Payoff under certainty 460,500

Expected Value of Perfect Information (EVPI) EVPI = Expected payoff under certainty - Maximum expected payoff. Our example: EVPI = $460,500-$455,000 = $5,500. This is the greatest amount of money the decision maker would be willing to pay to obtain perfect information about what demand will be.