McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 4 Decision Analysis Building the Structure for Solving the Problem

4-2 Decision Analysis Decision Making Under Uncertainty –Techniques play an important role in business, government, everyday life, college football rankings –How can a manager provide a rational methodology for decision making and analysis in the face of uncertainty? –How does a manager chose among alternatives in an optimal fashion when those alternatives may be numerous and conflicting ?

4-3 Components of Decision Making State –An actual event that may occur in the future Decision –Options from which a decision maker can chose Outcomes –The result of a combination of states and decisions

4-4 Payoff Table A means to organize states, decisions, and outcomes e.g., States Decisions a b 1payoff 1apayoff 1b 2 payoff 2apayoff 2b

4-5 Payoff Table Example An investor must decide among an apartment building, an office building, and a warehouse. States Decisions Good Bad Apartment $50,000$30,000 Office 100,000-40,000 Warehouse 30,000 10,000

4-6 Decision Criteria Maximax Maximin Minimax Regret Hurwicz Equal Likelihood

4-7 Maximax Decision maker selects the decision that will result in the maximum of the maximum payoffs Decisions Payoff Apartment $50,000 Office 100,000 Warehouse 30,000 Decision would be to purchase the office Decision completely ignores down side, loss of $40,000 Assumes a very optimistic future

4-8 Maximin Decision maker selects the decision that will result in the maximum of the minimum payoffs Decisions Bad Apartment $30,000 Office -40,000 Warehouse 10,000 Decision would be to purchase the apartment Decision is relatively conservative Assumes a very pessimistic future

4-9 Minimax Regret Decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret Select the maximum payoff under each state: –Good ----> $100,000 –Bad > 30,000 Regret is then calculated as follows: –Good ----> $100,000 - payoff for each decision –Bad > 30,000 - payoff for each decision

4-10 Minimax Regret The calculations for the example States DecisionsGood Bad Apartment $100, ,000 = 50,000 $30, ,000 = 0 Office$100, ,000 = 0$30,000 - (-40,000) = 70,000 Warehouse $100, ,000 = 70,000 $30, ,000 = 20,000 Chose the decision which minimizes this regret Purchase the apartment building Decision maker experiences the least amount of regret

4-11 Hurwicz Criterion A compromise between the maximax and maximin criterions Payoffs are weighted using a coefficient of optimism,  A measure of the decision maker’s optimism regarding the outcome of the events 0 <  < 1

4-12 Hurwicz Criterion The  is multiplied by the best payoff and (1-  ) is multiplied by the worst payoff and these values are added together This criterion is a simple weighting scheme However,  must be determined by the decision maker and is completely subjective The Hurwicz Criterion is subjective

4-13 Hurwicz Criterion Given  = 0.4, then 1-  = 0.6, DecisionsValues Apartment $50,000*(0.4) + $30,000*(0.6) = $38,000 Office$100,000 *(0.4) - $40,000*(0.6)= $16,000 Warehouse $30,000 *(0.4) + $10,000*(0.6) = $18,000 Hurwicz criterion specifies selection corresponding to the maximum weighted average Apartment building

4-14 Equal Likelihood or LaPlace Criterion when  = 0.5, for our example DecisionsValues Apartment $50,000*(0.5) + $30,000*(0.5) = $40,000 Office$100,000 *(0.5) - $40,000*(0.5)= $30,000 Warehouse $30,000 *(0.5) + $10,000*(0.5) = $20,000 Equal likelihood criterion specifies selection corresponding to the maximum weighted average Apartment building

4-15 Limitations of Weighting Methods Regardless of how  is determined it is a subjective measure, even with equal likelihood The degree of the decision maker’s optimism is reflected in  Untrained decision maker’s generally choose  incorrectly How would you choose  ?

4-16 Summary of Techniques CriterionDecision MaximaxOffice Building MaximinApartment Minimax regretApartment HurwiczApartment Equal LikelihoodApartment

4-17 Decision Trees Useful to structure sequential decision making problems Useful in presence of uncertainty Related to: –Probability trees Chance nodes branch to states

4-18 Decision Tree Properties Describe choices and uncertainties facing a single decision maker (or company) Combine probability trees with decisions –Choice nodes –Decision nodes Assume competitors’ actions to be random

4-19 Framing Decision Tree Structures Determine essential decisions and chance outcomes Place in appropriate temporal sequence Start tree with a decision node Select a representative, but not exhaustive, list of outcomes for decision node For each outcome draw a chance node Select a representative, but not exhaustive, list of outcomes for each chance node Continue to expand the tree until a point where the overall outcome can be evaluated

4-20 Rolling Back a Decision Tree Start from last set of nodes For each chance node, calculate the expected value as a prob.-weighted average of the branches values –Replace each chance node by its expected value For each decision node, find the best value among the choices corresponding to the branches –Replace each decision node with best value and note which choice is best Continue evaluating chance and decision nodes, backward in sequence until first node is resolved

4-21 Influence Diagrams A tool for structuring relationships between variables –Bridges the gap between a problem and the mathematical equations used –Serves as a means to give physical structure to a computer model –Evolved from a decision tree, used in spreadsheet modeling

4-22 Influence Diagrams Used to display –decisions –intermediate variables –outcomes Influence means dependency of one variable on another Influence can be certain or uncertain

4-23 Influence Diagrams Rectangles –Decision variables Circle –intermediate variables Oval –signifies outcomes

4-24 Influence Diagrams Variables –Random variables are noted with a tilde (~) above the variable Arrows –Related variables are connected by arrows –Arrows indicate direction of influence –Indicate type of influence

4-25 Influence Diagrams Arrows –Single straight arrow indicates certain influence –For an hourly worker, hours worked influences the amount of pre-tax take home pay –If hours worked increases without question pre-tax take home pay should increase Hours worked Pre-Tax Pay

4-26 Influence Diagrams Arrows –An arrow with a bend or squiggle stands for uncertain influence –Price will affect sales, but the influence is uncertain –We would expect if price goes up sales would be lower, but by how much? Sales Price