1. Decision Theory Chapter 5 Supplement June 26, 2012

2. Productivity (chpt 2: 53-59 Definition P = output/input – Work produced/ (labor hours, # of workers, etc.) – Problem 2, page 62 WeekCrew SizeYds installedLabor Productivity 1496 2372 3492 4250 5369 6252

3. WeekCrew SizeYds installedLabor Productivity 1496 24 yds 237224 349223 425025 536923 625226

4. Multifactor productivity (Quantity of production)/ (multiple inputs, e.g., labor cost + materials costs + overhead) Problem 3, p 62 WeekOutput (in units)WorkersMaterial (lbs) 130,0006450 233,6007470 332,2007460 435,4008480

5. Labor costs Week 1 – 6 X $12 X 40 hrs = $2,880 Week 2 – 7 X $12 X 40 hrs = $3,360 Week 3 – 7 X $12 X 40 hrs = $3,360 Week 4 – 8 X $12 X 40 hrs = $3,840 TOTAL LABOR COSTS= $13,440

6. Overhead costs Week 1 – 1.5 X $2,880 = $4,320 Week 2 – 1.5 X $3,360 = $5,040 Week 3 – 1.5 X $3,360 = $5,040 Week 4 – 1.5 X $3,840 = $5,760 TOTAL OVERHEAD COSTS = $20,160

7. Material costs Week 1 – $6 X 450 = $2,700 Week 2 – $6 X 470 = $2,820 Week 3 – $6 X 460 = $2,760 Week 4 – $6 X 480 = $2,880 TOTAL MATERIAL COSTS = $11,160

8. WeekOutput (in units) Labor costs Overhead costs Material costs Total costs 130,000 233,600 332,200 435,400

9. WeekOutput (in units) Labor costs Overhead costs Material costs Total costs 130,000$2,880$4,320$2,700$9,900 233,600$3,360$5,040$2,820$11,240 332,200$3,360$5,040$2,760$11,160 435,400$3,840$5,760$2,880$12,480

10. WeekOutput (in units) Labor costs Overhead costs Material costs Total costs MFP$ productivity 130,000$2,880$4,320$2,700$9,900 233,600$3,360$5,040$2,820$11,240 332,200$3,360$5,040$2,760$11,160 435,400$3,840$5,760$2,880$12,480

11. WeekOutput (in units) Labor costs Overhead costs Material costs Total costs MFP$ productivity 130,000$2,880$4,320$2,700$9,9003.03 233,600$3,360$5,040$2,820$11,2402.99 332,200$3,360$5,040$2,760$11,1602.89 435,400$3,840$5,760$2,880$12,4802.84

12. WeekOutput (in units) Labor costs Overhead costs Material costs Total costs MFP$ productivity 130,000$2,880$4,320$2,700$9,9003.03$424.20 233,600$3,360$5,040$2,820$11,2402.99$418.60 332,200$3,360$5,040$2,760$11,1602.89$404.60 435,400$3,840$5,760$2,880$12,4802.84$397.60

13. Productivity

14. RPG Problem 6, p. 62 Current week – 160 units/40 hrs – Current productivity: 4 units/hr Previous week – 138 units/ 36 hrs – Previous productivity: 3.83 units/hr RGP – (4 units/hr – 3.83 units/hr) / 3.83 units/hr) =.044 – 4.4%

15. What is decision theory? Definition – Payoff table (certainty) – P. 159 POSSIBLE FUTURE DEMAND AlternativesLowModerateHigh Small facility$10 Medium facility 7 12 Large facility (4) 2 16

16. What is decision theory? Basic concepts – Certainty vs uncertainty – Utility values Ex: 1,000 units sold = utility of 1,000 – Or 50,000 (arbitrary decision) – Expected utility Probability X utility

17. Expected utility example Outcome 1: Utility = 100, probability = 75% Outcome 2: Utility = -40, probability = 25% Expected utility =  100 X.75 = 75  -40 X.25 = -10  75 + (-10) = 65

18. Decision making under uncertainty 4 possible decision criteria – Maximin Best “worst” payoff – Maximax Best possible payoff – Laplace Equally lightly – Minimax regret Minimize “regret”

19. Decision making under uncertainty Problem 1 (p. 173) Maximax – 80, Expand Maximin – 50, Do nothing NEXT YEAR’S DEMAND AlternativesLowHIGH Do nothing$50$60 Expand 20 80 Subcontract 40 70

20. Decision making under uncertainty Problem 1 Laplace – Now we have problem! NEXT YEAR’S DEMAND AlternativesLowHIGH Do nothing$50$60 Expand 20 80 Subcontract 40 70 ($20+$80)/2 = $50 ($50+$60)/2 = $55 ($40+$70)/2 = $55

21. Decision making under uncertainty Problem 1 Minimax regrets (opportunity losses) NEXT YEAR’S DEMAND AlternativesLowHIGH Do nothing$50$60 Expand 20 80 Subcontract 40 70

22. Decision making under uncertainty Problem 1 Minimax regrets – subcontract NEXT YEAR’S DEMAND AlternativesLowHIGHWORST Do nothing$50 - $50 = 0$80 – 60 = 20$20 Expand 50 – 20 = 30 80 – 80 = 0 30 Subcontract 50 – 40 = 10 80 – 70 = 10 10

23. Decision making under risk Problem 2(a) EMV (expected profit) EMV(Do nothing): 50(.3) + 60(.7) = $57 EMV(Expand): 20(.3) + 80(.7) = $62 EMV(Subcontract): 40(.3) + 70(.7) = $61 NEXT YEAR’S DEMAND AlternativesLow P(.30)HIGH P(.70) Do nothing$50$60 Expand 20 80 Subcontract 40 70

24. Decision making under risk Problem 2(c) Expected value of perfect information (EVPI) Expected payoff under certainty (EPC) – 50(.3) + 80(.7) = 71 Expected payoff under risk – PR (EMV – Expand) = 62 EVPI = 71 – 62 = 9 NEXT YEAR’S DEMAND AlternativesLow P(.30)HIGH P(.70) Do nothing$50$60 Expand 20 80 Subcontract 40 70

25. Decision trees

27. P5, p. 174

28. So what do we conclude? Subcontract – Small demand: (0.4) * (1.0) = 0.4 – Medium demand: (0.5) * (1.3) = 0.65 – Large demand: (0.1) * (1.8) = 0.18 – Total expected payoff: 0.4 + 0.65 + 0.18 = 1.23

30. So what do we conclude? Expand – Small demand: (0.4) * (1.5) = 0.6 – Medium demand: (0.5) * (1.6) = 0.8 – Large demand: (0.1) * (1.7) = 0.17 – Total expected payoff: 0.6 + 0.8 + 0.17 = 1.57

32. So what do we conclude? Build – Small demand: (0.4) * (1.4) = 0.56 – Medium demand: (0.5) * (1.1) = 0.55 – Large demand: (0.1) * (2.4) = 0.24 – Total expected payoff: 0.56 + 0.55 + 0.24 = 1.35

33. So what do we conclude? Subcontract – Total expected payoff: 0.4 + 0.65 + 0.18 = 1.23 Expand – Total expected payoff: 0.6 + 0.8 + 0.17 = 1.57 Build – Total expected payoff: 0.56 + 0.55 + 0.24 = 1.35

34. Problem 12, p. 176 Assume equal probabilities Omit the leasing option

35. 1 Build small Build large 2 Lease Expand Demand low(.50) Demand high(.50) $700 $100 $500 $40 $2,000 Demand low(.50) Demand high(.50)

36. Alternatives Maximin - best “worst” – Small: $500k – Large: $40K Maximax – best possible – Large: $2,000k

37. Lapace Small –.50($700) +.5($500) = $600 Large –.50($40) +.50($2,000) = $1,020

38. 1 Build small Build large 2 Lease Expand Demand low(.50) Demand high(.50) $700 $100 $500 $40 $2,000 Demand low(.50) Demand high(.50)

39. Minimax regret AlternativesLowHigh Build Small$700$500 Build Large$40$2,000 AlternativesLowHigh Build Small$700 - $700 = $0$2,000 - $500 = $1,500 Build Large$700 - $40 = $660$2,000 - $2,000 = $0