BUAD 306 Chapter 5 S Decision Theory Why

BUAD 306 Chapter 5 S – Decision Theory

Why DM is Important ¢ The act of selecting a preferred course of action among alternatives A KEY responsibility of Operations Managers l Some Decision Making techniques can be specific l Day-to-day decisions can be improved and made consistently by using logical approaches l

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

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

Terms: Alternatives ¢ ¢ Choices the business can make, given the state of nature or other information Examples: l l 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

Terms: Payoff Table Possible Future Demand Low Moderate High 100 100 Medium 70 120 Large (40) 20 160 Alternatives Small *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: l l 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 Possible Future Demand Low Moderate High 200 200 Medium 140 240 Large (80) 40 320 Alternatives Small *Present value in $ millions

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

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

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

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

Example: COST A B C X 150 50 160 Part A: Maximin, Maximax, Laplace Y 70 200 60 Z 130 110 100

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 l Sum up weighted values and selects the best payoff l

EMV Example: We have established likelihoods of future demand as follows: Low: . 60, Medium, . 30, High, . 10 Possible Future Demand Alternatives Small Low Moderate High 200 200 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 i. Phone 400 500 900 Both -300 1500

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

EMV Example: Low: . 60, Medium, . 30, High, . 10 Possible Future Demand Alternatives Small Low Moderate High 200 200 Medium 140 240 Large (80) 40 320 EVPI = Expected Payoff __ Under Certainty Expected Payoff 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 i. Phone 400 500 900 Both -300 1500

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

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 l Round Nodes – Probabilities of events l 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). l l l 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.