**Operations ManagementDecision-Making ToolsModule A** © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Outline** • The Decision Process in Operations • Fundamentals of Decision Making • Decision Tables • Decision Making under Uncertainty • Decision Making Under Risk • Decision Making under Certainty • Expected Value of Perfect Information (EVPI) • Decision Trees • A More Complex Decision Tree © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Learning Objectives** When you complete this chapter, you should be able to: Identify or Define: • Decision trees and decision tables • Highest monetary value • Expected value of perfect information • Sequential decisions Describe or Explain: • Decision making under risk • Decision making under uncertainty • Decision making under risk © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Models, and the Techniques of Scientific Management** • Can Help Managers To: • Gain deeper insight into the nature of business relationships • Find better ways to assess values in such relationships; and • See a way of reducing, or at least understanding, uncertainty that surrounds business plans and actions © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Steps to Good Decisions** • Define problem and influencing factors • Establish decision criteria • Select decision-making tool (model) • Identify and evaluate alternatives using decision-making tool (model) • Select best alternative • Implement decision • Evaluate the outcome © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Models** • Are less expensive and disruptive than experimenting with the real world system • Allow operations managers to ask “What if” types of questions • Are built for management problems and encourage management input • Force a consistent and systematic approach to the analysis of problems • Require managers to be specific about constraints and goals relating to a problem • Help reduce the time needed in decision making © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Limitations of Models** They • may be expensive and time-consuming to develop and test • are often misused and misunderstood (and feared) because of their mathematical and logical complexity • tend to downplay the role and value of nonquantifiable information • often have assumptions that oversimplify the variables of the real world © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Quantitative Analysis** Logic Historical Data Marketing Research Scientific Analysis Modeling Problem Decision Qualitative Analysis Emotions Intuition Personal Experience and Motivation Rumors The Decision-Making Process © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Outcomes** States of Nature Alternatives Decision Problem Ways of Displaying a Decision Problem • Decision trees • Decision tables © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Fundamentals of Decision Theory** The three types of decision models: • Decision making under uncertainty • Decision making under risk • Decision making under certainty © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Fundamentals of Decision Theory - continued** Terms: • Alternative: course of action or choice • State of nature: an occurrence over which the decision maker has no control Symbols used in decision tree: • A decision node from which one of several alternatives may be selected • A state of nature node out of which one state of nature will occur © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Favorable market** A state of nature node 1 Unfavorable market Construct large plant Favorable market A decision node Construct small plant 2 Unfavorable market Do nothing Getz Products Decision Tree © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Decision Table** States of Nature State 1 State 2 Alternatives Outcome 1 Outcome 2 Alternative 1 Outcome 3 Outcome 4 Alternative 2 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Decision Making Under Uncertainty** • Maximax - Choose the alternative that maximizes the maximum outcome for every alternative (Optimistic criterion) • Maximin - Choose the alternative that maximizes the minimum outcome for every alternative (Pessimistic criterion) • Equally likely - chose the alternative with the highest average outcome. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**States of Nature** Alternatives Favorable Unfavorable Maximum Minimum Row Market Market in Row in Row Average Construct $200,000 - $180,000 $200,000 - $180,000 $10,000 large plant Construct $100,000 - $20,000 $100,000 - $20,000 $40,000 small plant $0 $ 0 $0 $0 $0 Do nothing Maximax Maximin Equally likely Example - Decision Making Under Uncertainty © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**The Decisions** • The maximax choice is to construct a large plant. This is the maximum of the maximum number within each row or alternative. • The maximin choice is to do nothing. This is the maximum of the minimum number within each row or alternative. • The equally likely choice is to construct a small plant. This is the maximum of the average outcomes of each alternative. This approach assumes that all outcomes for any alternative are equally likely. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Decision Making Under Risk** • Probabilistic decision situation • States of nature have probabilities of occurrence • Select alternative with largest expected monetary value (EMV) • EMV = Average return for alternative if decision were repeated many times © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Number of states of nature** Value of Payoff N Probability of payoff EMV ( A ) = X P ( X ) * j i i = i 1 = + + + X P ( X ) X P ( X ) X P ( X ) * ... * * 1 1 2 2 N N Alternative i Expected Monetary Value Equation © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**States of Nature** Alternatives Favorable Unfavorable Expected Market Market P(0.5) value P(0.5) Construct $200,000 -$180,000 $10,000 large plant Construct $100,000 -$20,000 $40,000 Best choice small plant Do nothing $0 $0 $0 Example - Decision Making Under Uncertainty © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Expected Value of Perfect Information (EVPI)** • EVPI places an upper bound on what one would pay for additional information • EVPIis the expected value with certainty minus the maximum EMV © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Expected Value With Perfect Information (EV|PI)** © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Expected Value of Perfect Information** EVPI = Expected value under Certainty - maximum EMV © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Expected Value of Perfect Information** Favorable Market ($) Unfavorable Market ($) EMV Construct a large plant $20,000 -$180,000 200,000 Construct a small plant $40,000 $100,000 -$20,000 Do nothing $0 $0 $0 0.50 0.50 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Expected Value of Perfect Information** EVPI = expected value with perfect information - max(EMV) = $200,000*0.50 + 0*0.50 - $40,000 = $60,000 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Decision Trees** • Graphical display of decision process • Used for solving problems • With one set of alternatives and states of nature, decision tables can be used also • With several sets of alternatives and states of nature (sequential decisions), decision tables cannot be used • EMV is criterion most often used © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Analyzing Problems with Decision Trees** • Define the problem • Structure or draw the decision tree • Assign probabilities to the states of nature • Estimate payoffs for each possible combination of alternatives and states of nature • Solve the problem by computing expected monetary values for each state-of-nature node © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**State 1** Outcome 1 1 State 2 Outcome 2 Alternative 1 State 1 Alternative 2 Outcome 3 2 State 2 Outcome 4 Decision Node State of Nature Node Decision Tree © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**EMV for node 1 = $10,000** Favorable market (0.5) 1 Unfavorable market (0.5) Construct large plant Favorable market (0.5) Construct small plant 2 Unfavorable market (0.5) Do nothing EMV for node 2 = $40,000 Getz Products Decision TreeCompleted and Solved Payoffs $200,000 -$180,000 $100,000 -20,000 0 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458

**Fav. Mkt (0.78)** 2nd decision point $106,000 1st decision point $190,000 -$190,000 $90,000 $30,000 $10,000 2 Unfav. Mkt (0.22) Large plant $63,600 Small plant $106,400 Fav. Mkt (0.78) 3 Unfav. Mkt (0.22) Sur. Res. Pos. (.45) No plant -$87,400 Fav. Mkt (0.27) $190,000 -$190,000 $90,000 $30,000 $10,000 1 4 Unfav. Mkt (0.73) Sur. Res. Neg. (.55) Large plant Survey Fav. Mkt (0.27) $2,400 Small plant $2,400 5 Unfav. Mkt (0.73) No plant $49,200 $10,000 Fav. Mkt (0.5) $200,000 -$180,000 $100,000 $20,000 $0 6 Unfav. Mkt (0.5) No survey Large plant $40,000 Fav. Mkt (0.5) Small plant $40,000 7 Unfav. Mkt (0.5) No plant Getz Products Decision Tree with Probabilities and EMVs Shown © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458