5s-1Decision Theory CHAPTER 5s Decision Theory McGraw-Hill/Irwin Operations Management, Eighth Edition, by William J. Stevenson Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.

5s-2Decision Theory Decision Theory represents a general approach to decision making which is suitable for a wide range of operations management decisions, including: product and service design equipment selection location planning Decision Theory Capacity planning

5s-3Decision Theory  A set of possible future conditions exists that will have a bearing on the results of the decision  A list of alternatives for the manager to choose from  A known payoff for each alternative under each possible future condition Decision Theory Elements

5s-4Decision Theory  Identify possible future conditions called states of nature  Develop a list of possible alternatives, one of which may be to do nothing  Determine the payoff associated with each alternative for every future condition Decision Theory Process

5s-5Decision Theory  If possible, determine the likelihood of each possible future condition  Evaluate alternatives according to some decision criterion and select the best alternative Decision Theory Process (Cont’d)

5s-6Decision Theory ADVANTAGES  USES UNCERTAINTY (OR PROBABILITY) ESTIMATES  CONSIDERS ALL POSSIBLE OUTCOMES ASSOCIATED WITH ALL POSSIBLE STATES OF NATURE  CONSIDERS COSTS ASSOCIATED WITH UNDER- AND OVER- UTILIZATION  CALCULATES EXPECTED VALUES FOR EACH ALTERNATIVE DISADVANTAGES  STATES OF NATURE ARE DISCRETE AND NON-OVERLAPPING  ARE PROBABILITIES RELIABLE? PRIMARILY USED WITH SINGLE-PHASE, RECURRING DECISIONS Payoff Tables

5s-7Decision Theory ADVANTAGES  USES PROBABILITIES TO REDUCE UNCERTAINTY  CALCULATES AN EXPECTED VALUE FOR EACH DECISION  USED TO GRAPHICALLY ILLUSTRATE COMPLEX, MULTI- PHASE DECISIONS DISADVANTAGES  EXPECTED VALUES ARE RELATIVE MEASURES, THEY AREN’T ABSOLUTE  RELIABILITY OF PROBABILITIES IS QUESTIONNABLE PRIMARILY USED WITH MULTI-PHASE, ONE-SHOT DECISIONS Decision Trees

5s-8Decision Theory  Certainty - Environment in which relevant parameters have known values  Risk - Environment in which certain future events have probable outcomes  Uncertainty - Environment in which it is impossible to assess the likelihood of various future events Decision Environments

5s-9Decision Theory Maximax - Choose the alternative with the best possible payoff Maximin - Choose the alternative with the best of the worst possible payoffs Minimax Regret - Chooe the alternative that has the least of the worst regrets Laplace - Choose the alternative with the best average payoff of any of the alternatives Decision Making under Uncertainty

5s-10Decision Theory A PAYOFF TABLE ILLUSTRATION EXPECTED PROFITS / ACRE STATES OF NATURE / ENVIRONMENTAL SCENARIOS ALTERNATIVE CROPS NORMAL WETDRYVIOLENT CORN POTATOES HAY/GRASS

5s-11Decision Theory A PAYOFF TABLE ILLUSTRATION UNDER TOTAL UNCERTAINTY EXPECTED PROFITS / ACRE STATES OF NATURE / ENVIRONMENTAL SCENARIOS ALTERNATIVE CROPS NORMAL WETDRYVIOLENT CORN POTATOES HAY/GRASS MAXI-MAX (Optimist) *Corn 900, Potato 800, Hay MAXI-MIN (Pessimist) Corn -800, Potato -300, *Hay 0 3. MINI-MAX (Regret) Regrets..Corn 1200, Potato 800, *Hay AVERAGE (Rational) Ex Value…Corn 200, *Potato 350, Hay 225

5s-12Decision Theory BUILDING A REGRET MATRIX EXPECTED PROFITS / ACRE STATES OF NATURE / ENVIRONMENTAL SCENARIOS ORIGINAL MATRIX ALTERNATIVE CROPS NORMAL WETDRYVIOLENT CORN POTATOES HAY/GRASS REGRET MATRIX CORN POTATOES HAY/GRASS MINIMIZE THE MAXIMUM REGRETS Corn = 1200, Potatoes = 800, Hay = 600**

5s-13Decision Theory A PAYOFF TABLE ILLUSTRATION UNDER RISK (ASSIGNED PROBABILITY) EXPECTED PROFITS / ACRE PROBABILITIES COME FROM “GOOD” GUESSES. CALCULATE THE EXPECTED VALUES INDIAN JOE’S ESTIMATES = Normal 30%, Wet 25%, Dry 20%, Violent 25% STATES OF NATURE / ENVIRONMENTAL SCENARIOS ALTERNATIVE CROPSNORMAL WETDRY VIOLENT EXPECTED WEIGHTS VALUES = = = = = = = = = = = = = = = = = = = = = = = CORN POTATOES ** HAY/GRASS = = = = = = = = = = = = = = = = = = = = = = = == = You should PLANT POTATOES EVERY YEAR. In any one year you’ll either make 800, lose 300, make 400, or make 500 …but over the years, you’ll average 370 of profits.

5s-14Decision Theory A PAYOFF TABLE ILLUSTRATION UNDER RISK (FACTUAL PROBABILITY) EXPECTED PROFITS / ACRE PROBABILITY INFORMATION COMES FROM RELIABLE (FACTUAL) SOURCES WEATHER BUREAU HISTORY = Normal 35%, Wet 30%, Dry 15%, Violent 20% STATES OF NATURE / ENVIRONMENTAL SCENARIOS ALTERNATIVE CROPS NORMAL WETDRY VIOLENT EXPECTED WEIGHTS VALUES = = = = = = = = = = = = = = = = = = = = = = = CORN ** POTATOES HAY/GRASS = = = = = = = = = = = = = = = = = = = = = = = You should PLANT CORN EVERY YEAR. In any one year you’ll either make 900, make 450, lose 800 or make 250 …but over the years, you’ll average 380 of profits.

5s-15Decision Theory Expected Value of Perfect Information Expected value of perfect information: the difference between the expected payoff under certainty and the expected payoff under risk Expected value of perfect information Expected payoff under certainty Expected payoff under risk = -

5s-16Decision Theory A PAYOFF TABLE ILLUSTRATION UNDER RISK (WHAT IS THE VALUE OF PERFECT INFORMATION?) WE KNOW ONLY GOD CONTROLS THE WEATHER, BUT IF WE HAD PERFECT PREDICTION EACH YEAR, WE’D KNOW EXACTLY WHAT THE WEATHER WOULD BE AND WHAT WE SHOULD PLANT. WE’D HAVE NORMAL CONDITIONS 35% OF THE TIME, AND DURING THOSE TIMES, WE’D PLANT CORN. 30% OF THE TIME IT WOULD BE WET AND WE’D PLANT HAY, ETC. STATES OF NATURE / ENVIRONMENTAL SCENARIOS ALTERNATIVE CROPS NORMAL WETDRY VIOLENT EXPECTED WEIGHTS VALUES = = = = = = = = = = = = = = = = = = = = = = = CORN ** POTATOES HAY/GRASS = = = = = = = = = = = = = = = = = = = = = = = Expected Profits given Perfect Information (EPPI) = 625. Expected Value of Perfect Information (EVPI) = EPPI – EV = 625 –380 = 245 Therefore, you can increase your profits by up to 245 if you have a perfect weather forecast each spring.

5s-17Decision Theory Format of a Decision Tree State of nature 1 B Payoff 1 State of nature 2 Payoff 2 Payoff 3 2 Choose A’ 1 Choose A’ 2 Payoff 6 State of nature 2 2 Payoff 4 Payoff 5 Choose A’ 3 Choose A’ 4 State of nature 1 Choose A’ Choose A’ 2 1 Decision Point Chance Event Figure 5S.1