BUAD306 Chapter 5S – Decision Theory

Why DM is Important The act of selecting a preferred course of action among alternatives A KEY responsibility of Operations Managers

DM Applications Some Decision Making techniques can be specific: Capacity planning Location planning Lease/Buy But in general, we can improve Decision Making by using logical approaches

How do WE make decisions? Alternatives? Likelihoods? Outcomes?

Reasons for Poor DM There may be better choices that have not been considered Information about options may be imperfect Knowledge of existing circumstances may be imperfect Past experience may be irrelevant Prediction of the future may be wrong Chains of cause and effect are subject to high probability of error Too much Information Peer Pressure

DM Steps 1.Identify possible future conditions (states of nature) 2.Develop a list of alternatives 3.Determine the estimated payoff for each alternative for every condition 4.Estimate the likelihood of each possible condition 5.Evaluate alternatives according to some criterion and select best alternative

States of Nature Possible outcomes that your business may experience Examples: Demand: High, Medium, Low Contracts: Awarded, Not Awarded Weather: Rainy, Mixed, Dry

Alternatives Choices the business can make, given the state of nature or other information Examples: Demand: Purchase new machinery, Don’t purchase machinery Contracts: Hire Additional Staff, Don’t Hire Weather: Invest in Irrigation System, Don’t Invest Do Nothing

Payoff Table *Present value in $ millions (Page 180 in text) Alternatives Possible Future Demand LowModerateHigh Small100 Medium70120 Large(40)20160

Likelihoods of Conditions Estimates of likelihood Typically stated in percentages, must total to 1.0 Based on historical data or subjective Examples: Demand: High (50%), Medium (30%), Low (20%) Weather: Rainy (30%), Mixed (40%), Dry (30%)

Decision Environments Certainty - Environment in which future events will definitely occur Uncertainty - Environment in which it is impossible to assess the likelihood of various future events Risk - Environment in which certain future events have probable outcomes Different environments require different analysis techniques!

DM Under Certainty When you know for sure which of the future conditions will occur, choose the alternative with the highest payoff!

DM Under Certainty Example *Present value in $ millions (Page 180 in text) We know for sure demand will be a) low, b) moderate, c) high Alternatives Possible Future Demand LowModerateHigh Small100 Medium70120 Large(40)20160

DM Under Uncertainty Maximin  Maximax Laplace  You don’t need to know Minimax Regret or Opportunity Loss Tables.

Maximin  “The best of the worst” Determine the worst possible payoff for each alternative, then Choose the alternative that is the “best worst”. Alts Possible Future Demand Maximin LowModerateHigh Small100 Medium70120 Large(40)20160

Maximax “The best of the best” Determine the best possible payoff for each alternative, then Choose the alternative that is the “best of the best”. Alts Possible Future Demand Maximax LowModerateHigh Small100 Medium70120 Large(40)20160

Laplace  “The best average” Determine the average payoff for each alternative, then Choose the alternative that is the “best average”. Alts Possible Future Demand Laplace LowModerateHigh Small100 Medium70120 Large(40)20160

AltLowModHigh Droid iPhone Both Decision Under Uncertainty Example: A Product Manager for a handheld software company is trying to decide whether to create an application for the Droid, iPhone or both devices. The revenue associated with each alternative depends on the demand for the product as noted below. What is the Maximin choice? What is the Maximax choice? What is the LaPlace choice?

Decision Under Uncertainty Example: A Product Manager for a handheld software company is trying to decide whether to create an application for the Droid, iPhone or both devices. The revenue associated with each alternative depends on the demand for the product as noted below. AltLowModHigh MaximinMaximaxLaplace Droid iPhone Both

XYZ A B C Example: COST Part A: Maximin, Maximax, Laplace

DM Under Risk Most typical in business Incorporates likelihoods into the process Allows you to weight payoffs by the probability that the state of nature will occur

Expected Monetary Value The best expected value among the alternatives Steps: For each cell in the Payoff Table, multiple the value by the likelihood of that state of nature Sum up weighted values and selects the best payoff

We have established likelihoods of future demand as follows: Low:.40, Medium,.50, High,.10 EMV Example: Alternatives Possible Future Demand LowModerateHigh Small100 Medium70120 Large(40)20160

Going back to our handheld application example, we now have the following likelihoods of future demand: Low: 30%, Moderate: 50% and High: 20% What are the EMVs for each alternative? EMV Example: EMV Droid EMV iPhone EMV Combo AltLowModHigh Droid iPhone Both

XYZ A B C Example: COST Part B: Assume the following likelihoods: X=.5, Y =.2, Z =.3

Expected Value of Perfect Information (EVPI) What if you could delay your decision until you had more data? Would you?? How much would you be willing to pay for that extra time? EVPI allows you to determine that figure

Calculating EVPI Want to know if the cost of obtaining the perfect information will be less than the expected gain due to delaying your decision. Therefore: EVPI =Expected Payoff Under Certainty Under Risk (EMV)

EMV Example: EVPI = Expected Payoff __Expected Payoff Under Certainty Under Risk Expected Payoff Under Certainty: Expected Payoff Under Risk: EVPI = Alternatives Possible Future Demand LowModerateHigh Small100 Medium70120 Large(40)20160 Low:.40, Medium,.50, High,.10

Going back to our handheld application example, we now have the following likelihoods of future demand: Low: 30%, Moderate: 50% and High: 20% What is the EVPI for this scenario? EMV Example: Expected Payoff Under Certainty = Expected Payoff Under Risk = Expected Value of Perfect Information = AltLowModHigh Droid iPhone Both

XYZ A B C Example: COST Part C: EVPI

Decision Trees Schematic representation Helpful in analyzing sequential decisions Can see all the options in front of you and compare easily

Decision Tree Lingo Nodes – Square Nodes - Make a decision Round Nodes – Probabilities of events Branches – contain information re: that decision or state of nature Right to Left Analysis Tree Pruning

Should we run the light?

HW #9 Firm must decide to build: Small, Medium or Large facility. Demand for all sizes could be low (.2) or high (.8). If build small and demand is low, NPV = $42. If demand is high, can subcontract (NPV = $42) or expand greatly (NPV = $48) If build medium and demand is low, NPV = $22. If demand is high, can do nothing (NPV = $46) or expand greatly (NPV = $50) If build large and demand is low, NPV = -$20. If demand is high, NPV = $72.