Chapter 5S – Decision Theory 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 Some Decision Making techniques can be specific Day-to-day decisions can be improved and made consistently by using logical approaches

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

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

Terms: 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

Possible Future Demand Present value in $ millions Terms: Payoff Table Alternatives Possible Future Demand Low Moderate High Small 100 Medium 70 120 Large (40) 20 160 Present value in $ millions (Page 180 in text)

Terms: Likelihoods Probability of state of nature 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 We know for sure demand will be a) low, b) moderate, c) high Alternatives Possible Future Demand Low Moderate High Small 200 Medium 140 240 Large (80) 40 320 Present value in $ millions

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

Possible Future Demand 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 Low Moderate High Small 200 Medium 140 240 Large (80) 40 320

Possible Future Demand 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 Low Moderate High Small 200 Medium 140 240 Large (80) 40 320

Possible Future Demand Laplace  “The best average” Determine the average payoff for each alternative, then Choose the alternative that is the “best average”. Alts Possible Future Demand Low Moderate High Small 200 Medium 140 240 Large (80) 40 320

Decision Under Uncertainty Example: A Product Manager for a phone software company is trying to decide whether to create an app for the Droid, iPhone or both platforms. The revenue associated with each alternative depends on the demand for the app as noted below. Alt Low Mod High Droid 300 600 1000 iPhone 400 500 900 Both -300 1500 What is the Maximin choice? What is the Maximax choice? What is the LaPlace choice?

Example: COST X Y Z A 150 70 130 B 50 200 110 C 160 60 100 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

Alternatives Possible Future Demand EMV Example: We have established likelihoods of future demand as follows: Low: .60, Medium, .30, High, .10 Alternatives Possible Future Demand Low Moderate High Small 200 Medium 140 240 Large (80) 40 320

EMV Example: 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? Alt Low Mod High Droid 300 600 1000 iPhone 400 500 900 Both -300 1500

Example: COST X Y Z A 150 70 130 B 50 200 110 C 160 60 100 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 Expected Payoff Under Certainty Under Risk (EMV)

Possible Future Demand EMV Example: Low: .60, Medium, .30, High, .10 Alternatives Possible Future Demand Low Moderate High Small 200 Medium 140 240 Large (80) 40 320 EVPI = Expected Payoff __ Expected Payoff Under Certainty Under Risk

EMV Example: 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? Alt Low Mod High Droid 300 600 1000 iPhone 400 500 900 Both -300 1500

Example: COST X Y Z A 150 70 130 B 50 200 110 C 160 60 100 Part C: EVPI .5, .2, .3

Zero EVPI? What does it mean? Example (revenue) Lo Mod Hi X 150 100 130 Y 50 80 90 Z 110 75 Likelihoods: Lo: .5, Mod: .2, Hi: .3

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.

Analysis with Decision Trees Certainty? Maximin, Maximax, LaPlace? EMV EVPI?