Supplement S2

1. 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

3. Decision Making • States of nature • Events that may occur in the future • Decision maker is uncertain which state of nature will occur • Decision maker has no control over the states of nature

4. Payoff Table • A method of organizing & illustrating the payoffs from different decisions given various states of nature • A payoff is the outcome of the decision

5. Payoff Table States Of Nature Decision a b 1 Payoff 1a Payoff 1b 2 Payoff 2a Payoff 2b Table S2.1

6. Decision Making Criteria Under Uncertainty • Maximax criterion • Choose decision with the maximum of the maximum payoffs • Maximin criterion • Choose decision with the maximum of the minimum payoffs • Minimax regret criterion • Choose decision with the minimum of the maximum regrets for each alternative

7. Hurwicz criterion • 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) • Equal likelihood (La Place) criterion • Choose decision in which each state of nature is weighted equally

8. STATES OF NATURE Good Foreign Poor Foreign DECISION Competitive Conditions Competitive Conditions Expand $ 800,000 $ 500,000 Maintain status quo 1,300,000 -150,000 Sell now 320,000 320,000 Southern Textile Company Example S2.1

9. STATES OF NATURE Good Foreign Poor Foreign DECISION Competitive Conditions Competitive Conditions Expand $ 800,000 $ 500,000 Maintain status quo 1,300,000 -150,000 Sell now 320,000 320,000 Southern Textile Company Example S2.1 Maximax Solution Expand: $800,000 Status quo: 1,300,000 Maximum Sell: 320,000 Decision: Maintain status quo

10. STATES OF NATURE Good Foreign Poor Foreign DECISION Competitive Conditions Competitive Conditions Expand $ 800,000 $ 500,000 Maintain status quo 1,300,000 -150,000 Sell now 320,000 320,000 Southern Textile Company Example S2.1 Maximin Solution Expand: $500,000 Maximum Status quo: -150,000 Sell: 320,000 Decision: Expand

11. STATES OF NATURE Good Foreign Poor Foreign DECISION Competitive Conditions Competitive Conditions Minimax Regret Solution $1,300,000 - 800,000 = 500,000 $500,000 - 500,000 = 0 1,300,000 - 1,300,000 = 0 500,000 - (-150,000) = 650,000 1,300,000 - 320,000 = 980,000 500,000 - 320,000 = 180,000 GOOD CONDITIONS POOR CONDITIONS Expand $ 800,000 $ 500,000 Maintain status quo 1,300,000 -150,000 Sell now 320,000 320,000 Expand: $500,000 Minimum Status quo: 650,000 Sell: 980,000 Decision: Expand Southern Textile Company Example S2.1

12. STATES OF NATURE Good Foreign Poor Foreign DECISION Competitive Conditions Competitive Conditions Expand $ 800,000 $ 500,000 Maintain status quo 1,300,000 -150,000 Sell now 320,000 320,000 Southern Textile Company Example S2.1 Hurwicz Criteria  = 0.3 1 -  = 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. STATES OF NATURE Good Foreign Poor Foreign DECISION Competitive Conditions Competitive Conditions Expand $ 800,000 $ 500,000 Maintain status quo 1,300,000 -150,000 Sell now 320,000 320,000 Southern Textile Company 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. Decision Making with Probabilities • 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

15. n i =1 EV (x) = p(xi)xi  Expected Value where xi = outcome i p(xi) = probability of outcome i

16. STATES OF NATURE Good Foreign Poor Foreign DECISION Competitive Conditions Competitive Conditions Expand $ 800,000 $ 500,000 Maintain status quo 1,300,000 -150,000 Sell now 320,000 320,000 Southern Textile Company 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. Expected Value of Perfect Information • The maximum value of perfect information to the decision maker • EVPI = (expected value given perfect information) - (expected value without perfect information)

18. EVPI Example • 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 • Expected value given perfect information= $1,300,000 (0.70) + 500,000 (0.30) = $1,060,000EVPI =$1,060,000 - 865,000 = $195,000

19. Sequential Decision Trees • A graphical method for analyzing decision situations that require a sequence of decisions over time • Decision tree consists of • Square nodes - indicating decision points • Circles nodes - indicating states of nature • Arcs - connecting nodes

20. Southern Textile Decision Tree Example S2.3

21. $2,000,000 0.60 Market growth 2 0.40 No market growth $225,000 Market growth $3,000,000 Expand (-$800,000) Expand (-$800,000) 0.80 6 $700,000 0.20 4 1 Market growth (3 years, $0 payoff) No market growth Sell land Purchase Land (-$200,000) 0.60 $2,300,000 Market growth 3 0.40 Warehouse (-$600,000) 0.30 7 $1,000,000 0.70 5 No market growth (3 years, $0 payoff) No market growth Sell land Example S2.3 $210,000 Southern Textile Decision Tree

22. Evaluations at Nodes Compute EV at nodes 6 & 7 EV(node 6) = 0.80($3,000,000) + 0.20($700,000) = $2,540,000EV(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. $2,000,000 0.60 Market growth 2 0.40 No market growth $225,000 Market growth $3,000,000 Expand (-$800,000) Expand (-$800,000) 0.80 6 $700,000 0.20 4 1 Market growth (3 years, $0 payoff) No market growth Sell land Purchase Land (-$200,000) 0.60 $2,300,000 Market growth 3 0.40 Warehouse (-$600,000) 0.30 7 $1,000,000 0.70 5 No market growth (3 years, $0 payoff) No market growth Sell land Example S2.3 $210,000 Decision Tree Solution

24. $2,000,000 $1,290,000 0.60 Market growth 2 0.40 No market growth $225,000 Market growth $3,000,000 $2,540,000 Expand (-$800,000) Expand (-$800,000) 0.80 6 $1,740,000 $700,000 0.20 4 1 $1,160,000 Market growth (3 years, $0 payoff) No market growth Sell land Purchase Land (-$200,000) 0.60 $2,300,000 Market growth $1,390,000 3 0.40 Warehouse (-$600,000) 0.30 $790,000 7 $1,360,000 $1,000,000 0.70 5 No market growth (3 years, $0 payoff) No market growth Sell land Example S2.3 $210,000 Decision Tree Solution

25. Decision Analysis Exhibit S2.1

26. Decision Analysis Exhibit S2.2

27. Decision Analysis Formula for expected value computed in cell D6 Exhibit S2.3

28. Decision Analysis Click on “OM” to access Decision Table macro. Enter problem parameters in cells B8:C11. Exhibit S2.4