Decision Theory Chapter 5 Supplement June 26, 2012

Productivity (chpt 2: Definition P = output/input – Work produced/ (labor hours, # of workers, etc.) – Problem 2, page 62 WeekCrew SizeYds installedLabor Productivity

WeekCrew SizeYds installedLabor Productivity yds

Multifactor productivity (Quantity of production)/ (multiple inputs, e.g., labor cost + materials costs + overhead) Problem 3, p 62 WeekOutput (in units)WorkersMaterial (lbs) 130, , , ,

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

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

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

WeekOutput (in units) Labor costs Overhead costs Material costs Total costs 130, , , ,400

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

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

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

WeekOutput (in units) Labor costs Overhead costs Material costs Total costs MFP$ productivity 130,000$2,880$4,320$2,700$9, $ ,600$3,360$5,040$2,820$11, $ ,200$3,360$5,040$2,760$11, $ ,400$3,840$5,760$2,880$12, $397.60

Productivity

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%

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

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

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

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

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 Subcontract 40 70

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

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

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 = – 80 = 0 30 Subcontract 50 – 40 = – 70 = 10 10

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 Subcontract 40 70

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 Subcontract 40 70

Decision trees

P5, p. 174

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: = 1.23

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: = 1.57

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: = 1.35

So what do we conclude? Subcontract – Total expected payoff: = 1.23 Expand – Total expected payoff: = 1.57 Build – Total expected payoff: = 1.35

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

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)

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

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

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)

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