Chapter 5: Decision-making Concepts Quantitative Decision Making with Spreadsheet Applications 7 th ed. By Lapin and Whisler

Decision Theory Making a choice from a set of alternatives. Making a choice from a set of alternatives. Analyze which alternative optimizes outcome. Analyze which alternative optimizes outcome. Uses probability and statistics. Uses probability and statistics. Want a system for making the best choice. Want a system for making the best choice. Payoff table Payoff table Decision tree Decision tree

Certainty Decision making under certainty involves making a choice where all outcomes are determined solely by the choice you make. Decision making under certainty involves making a choice where all outcomes are determined solely by the choice you make. Example: Choosing what to wear. Example: Choosing what to wear.

Uncertainty Decision making under uncertainty involves making a choice where the outcomes are only partially determined by choice. This is more complex. Decision making under uncertainty involves making a choice where the outcomes are only partially determined by choice. This is more complex. Example: Whether to carry an umbrella (or rain jacket). Example: Whether to carry an umbrella (or rain jacket).

Acts, Outcomes, and Events Acts are the decision maker’s choices. Acts are the decision maker’s choices. Outcomes are the success of the decision (level of enjoyment, amount of profit, etc) Outcomes are the success of the decision (level of enjoyment, amount of profit, etc) Events are the uncertainty that can occur in some situations. Events are the uncertainty that can occur in some situations.

Example Choose what to wear. Choose what to wear. Acts – available outfits. Acts – available outfits. Outcomes – how good you look. Outcomes – how good you look. Should you carry an umbrella? Should you carry an umbrella? Act – carry an umbrella or don’t. Act – carry an umbrella or don’t. Event – It rains or it doesn’t Event – It rains or it doesn’t Outcomes – depend on both the act and the event. Outcomes – depend on both the act and the event.

Decision Table (p.124) EventAct Carry Umbrella Don’t Carry Umbrella Rain Stay Dry Get Wet No rain Carry something extra you don’t need Be dry and free

Carry Umbrella Don’t Carry Umbrella Rain No Rain Rain No Rain Stay Dry Carry something extra you don’t need Get Wet Be dry and free Decision Tree

Some Terms to Know Two measures: Two measures: Uncertainty Uncertainty Comparative worth/Payoff Comparative worth/Payoff

Example (p.127) Choosing a Movement for Tippi- Toes A toy manufacturer must choose among four prototype designs for Tippi-Toes, a dancing ballerina doll. Each prototype represents a different technology. One is a complete arrangement of gears and levers. The second is similar, but it uses springs. Another works on the principle of weights and pulleys. The fourth design is controlled pneumatically through a series of valves.

Choice of movement designs is based solely on comparison of the contributions to profits made by the four prototypes. Choice of movement designs is based solely on comparison of the contributions to profits made by the four prototypes. Only the following three events will be considered: Light demand(25,000 units), Moderate demand (100,000 units) or Heavy demand (150,000 units). Only the following three events will be considered: Light demand(25,000 units), Moderate demand (100,000 units) or Heavy demand (150,000 units).

Example Event (level of demand) Act (choice of movement) Gears and Levers Spring Action Weights and Pulleys Pneumatic Light$25,000-$10,000-$125,000-$300,000 Moderate$400,000$440,000$400,000$300,000 Heavy$650,000$740,000$750,000$700,000

Reducing the number of alternatives An act that is dominated by another is an inadmissable act. If every entry in a single column of the payoff table is less than or equal to the corresponding entry in a column of another act then it is an inadmissable act. The remaining acts are admissable acts. An act that is dominated by another is an inadmissable act. If every entry in a single column of the payoff table is less than or equal to the corresponding entry in a column of another act then it is an inadmissable act. The remaining acts are admissable acts.

Example 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$400,000 Heavy$650,000$740,000$750,000

Maximizing Expected Payoff: The Bayes Decision Rule Suppose the following probabilities are associated to the demand for Tippi-Toes: Suppose the following probabilities are associated to the demand for Tippi-Toes: Light demand.10 Light demand.10 Moderate demand.70totals to 1.00 Moderate demand.70totals to 1.00 Heavy demand.20 Heavy demand.20

Event (level of demand) Probability Act (Choice of Movement) Gears & Levers Spring Action Weights & Pulleys Payoff Payoff x Prob Payoff Payoff Light.10$25,000$2500-$10,000-$1000-$125,000-$12,500 Moderat e.70400,000280,000440,000308,000400,000280,000 Heavy.20650,000130,000740,000148,000750,000150,000 ExpectedPayoff:$412,500$455,000$417,500