1. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Supplement S2 Decision Analysis To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved.

2. Decision Analysis A set of quantitative decision- making techniques for decision situations where uncertainty exists A set of quantitative decision- making techniques for decision situations where uncertainty exists

3. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Making States of nature States of nature Events that may occur in the future Events that may occur in the future Decision maker is uncertain which state of nature will occur Decision maker is uncertain which state of nature will occur Decision maker has no control over the states of nature Decision maker has no control over the states of nature

4. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Payoff Table A method of organizing & illustrating the payoffs from different decisions given various states of nature A method of organizing & illustrating the payoffs from different decisions given various states of nature A payoff is the outcome of the decision A payoff is the outcome of the decision

5. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Payoff Table States Of Nature Decisionab 1Payoff 1aPayoff 1b 2Payoff 2aPayoff 2b Table S2.1

6. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Making Criteria Under Uncertainty Maximax criterion Maximax criterion Choose decision with the maximum of the maximum payoffs Choose decision with the maximum of the maximum payoffs Maximin criterion Maximin criterion Choose decision with the maximum of the minimum payoffs Choose decision with the maximum of the minimum payoffs Minimax regret criterion Minimax regret criterion Choose decision with the minimum of the maximum regrets for each alternative Choose decision with the minimum of the maximum regrets for each alternative

7. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Hurwicz criterion Hurwicz criterion Choose decision in which decision payoffs are weighted by a coefficient of optimism,  Choose decision in which decision payoffs are weighted by a coefficient of optimism,  Coefficient of optimism (  ) is a measure of a decision maker’s optimism, from 0 (completely pessimistic) to 1 (completely optimistic) Coefficient of optimism (  ) is a measure of a decision maker’s optimism, from 0 (completely pessimistic) to 1 (completely optimistic) Equal likelihood (La Place) criterion Equal likelihood (La Place) criterion Choose decision in which each state of nature is weighted equally Choose decision in which each state of nature is weighted equally

8. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300,000-150,000 Sell now320,000320,000 Example S2.1

9. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300,000-150,000 Sell now320,000320,000 Example S2.1 Maximax Solution Expand:$800,000 Status quo:1,300,000  Maximum Sell: 320,000 Decision: Maintain status quo

10. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300,000-150,000 Sell now320,000320,000 Example S2.1 Maximin Solution Expand:$500,000  Maximum Status quo:-150,000 Sell: 320,000 Decision: Expand

11. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300,000-150,000 Sell now320,000320,000 Example S2.1 Minimax Regret Solution $1,300,000 - 800,000= 500,000 $500,000 - 500,000= 0 1,300,000 - 1,300,000= 0500,000 - (-150,000)= 650,000 1,300,000 - 320,000= 980,000500,000 - 320,000= 180,000 GOOD CONDITIONSPOOR CONDITIONS Expand:$500,000  Minimum Status quo:650,000 Sell: 980,000 Decision: Expand

12. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300,000-150,000 Sell now320,000320,000 Example S2.1 Hurwicz Criteria  = 0.31 -  = 0.7 Expand: $800,000(0.3) + 500,000(0.7) = $590,000  Maximum Status quo: 1,300,000(0.3) -150,000(0.7) = 285,000 Sell: 320,000(0.3) + 320,000(0.7) = 320,000 Decision: Expand

13. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300,000-150,000 Sell now320,000320,000 Example S2.1 Equal Likelihood Criteria Two states of nature each weighted 0.50 Expand: $800,000(0.5) + 500,000(0.5) = $650,000  Maximum Status quo: 1,300,000(0.5) -150,000(0.5) = 575,000 Sell: 320,000(0.5) + 320,000(0.5) = 320,000 Decision: Expand

14. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Making with Probabilities Risk involves assigning probabilities to states of nature Risk involves assigning probabilities to states of nature Expected value is a weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence Expected value is a weighted average of decision outcomes in which each future state of nature is assigned a probability of occurrence

15. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Expected Value EV ( x ) = p ( x i ) x i n i =1 where x i = outcome i p ( x i )= probability of outcome i

16. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company STATES OF NATURE Good ForeignPoor Foreign DECISION Competitive ConditionsCompetitive Conditions Expand$ 800,000$ 500,000 Maintain status quo1,300,000-150,000 Sell now320,000320,000 Example S2.2 Expected Value p (good) = 0.70 p (poor) = 0.30 EV(expand) $800,000(0.7) + 500,000(0.3) = $710,000 EV(status quo) 1,300,000(0.7) -150,000(0.3) = 865,000  Maximum EV(sell) 320,000(0.7) + 320,000(0.3) = 320,000 Decision: Status quo

17. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Expected Value of Perfect Information The maximum value of perfect information to the decision maker The maximum value of perfect information to the decision maker EVPI = (expected value given perfect information) - (expected value without perfect information) EVPI = (expected value given perfect information) - (expected value without perfect information)

18. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. EVPI Example Good conditions will exist 70% of the time, choose maintain status quo with payoff of $1,300,000 Good conditions will exist 70% of the time, choose maintain status quo with payoff of $1,300,000 Poor conditions will exist 30% of the time, choose expand with payoff of $500,000 Poor conditions will exist 30% of the time, choose expand with payoff of $500,000 Expected value given perfect information = $1,300,000 (0.70) + 500,000 (0.30) = $1,060,000 EVPI= $1,060,000 - 865,000 = $195,000 Expected value given perfect information = $1,300,000 (0.70) + 500,000 (0.30) = $1,060,000 EVPI= $1,060,000 - 865,000 = $195,000

19. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Sequential Decision Trees A graphical method for analyzing decision situations that require a sequence of decisions over time A graphical method for analyzing decision situations that require a sequence of decisions over time Decision tree consists of Decision tree consists of Square nodes - indicating decision points Square nodes - indicating decision points Circles nodes - indicating states of nature Circles nodes - indicating states of nature Arcs - connecting nodes Arcs - connecting nodes

20. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Decision Tree Example S2.3

21. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Decision Tree 0.40 0.60 Warehouse(-$600,000) Sell land Marketgrowth 0.70 Marketgrowth 0.80 0.20 2 1 3 4 5 6 7 Expand(-$800,000) Purchase Land (-$200,000) Expand(-$800,000) 0.60 0.40 No market growth $225,000 Market growth $2,000,000$3,000,000 $700,000 $2,300,000 $1,000,000 $210,000 No market growth growth 0.30 growth (3 years, $0 payoff) Market growth (3 years, $0 payoff) Example S2.3

22. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Evaluations at Nodes Compute EV at nodes 6 & 7 EV(node 6)= 0.80($3,000,000) + 0.20($700,000) = $2,540,000 EV(node 7)= 0.30($2,300,000) + 0.70($1,000,000) = $1,390,000 Expected values written above nodes 6 & 7 Decision at node 4 is between $2,540,000 for Expand and $450,000 for Sell land Choose Expand Repeat expected value calculations and decisions at remaining nodes

23. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Tree Solution 2 1 3 4 5 6 7 Expand(-$800,000) Purchase Land (-$200,000) Expand(-$800,000) Warehouse(-$600,000) 0.60 0.40 No market growth $225,000 Market growth $2,000,000$3,000,000 $700,000 $2,300,000 $1,000,000 $210,000 Marketgrowth Marketgrowth No market growth growth Sell land 0.80 0.40 0.70 0.30 No market growth (3 years, $0 payoff) Market growth (3 years, $0 payoff) 0.20 0.60 Example S2.3

24. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Tree Solution 6 7 2 1 3 4 5 Expand(-$800,000) Purchase Land (-$200,000) $1,160,000 $1,360,000 $790,000 $1,390,000 $1,740,000 $2,540,000 Expand(-$800,000) Warehouse(-$600,000) 0.60 0.40 No market growth $225,000 Market growth $2,000,000$3,000,000 $700,000 $2,300,000 $1,000,000 $210,000 Marketgrowth Marketgrowth No market growth growth Sell land 0.80 0.40 0.70 0.30 No market growth (3 years, $0 payoff) Market growth (3 years, $0 payoff) $1,290,000 0.20 0.60 Example S2.3

25. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Analysis Exhibit S2.1

26. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Analysis Exhibit S2.2

27. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Analysis Exhibit S2.3 Formula for expected value computed in cell D6

28. To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Decision Analysis Exhibit S2.4 Enter problem parameters in cells B8:C11. Click on “OM” to access Decision Table macro.