Transcript Module 16 – Decision Theory

Decision Theory
Chapter 5 Supplement
June 26, 2012
Productivity (chpt 2: 53-59
• Definition
• P = output/input
– Work produced/ (labor hours, # of workers, etc.)
– Problem 2, page 62
Week
Crew Size
Yds installed
1
4
96
2
3
72
3
4
92
4
2
50
5
3
69
6
2
52
Labor Productivity
Week
Crew Size
Yds installed
Labor Productivity
1
4
96
24 yds
2
3
72
24
3
4
92
23
4
2
50
25
5
3
69
23
6
2
52
26
Multifactor productivity
• (Quantity of production)/
(multiple inputs, e.g., labor cost + materials costs +
overhead)
• Problem 3, p 62
Week
Output (in units)
Workers
Material (lbs)
1
30,000
6
450
2
33,600
7
470
3
32,200
7
460
4
35,400
8
480
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
Week
Output
(in units)
1
30,000
2
33,600
3
32,200
4
35,400
Labor
costs
Overhead
costs
Material
costs
Total
costs
Week
Output
(in units)
Labor
costs
Overhead
costs
Material
costs
Total
costs
1
30,000
$2,880
$4,320
$2,700
$9,900
2
33,600
$3,360
$5,040
$2,820
$11,240
3
32,200
$3,360
$5,040
$2,760
$11,160
4
35,400
$3,840
$5,760
$2,880
$12,480
Week
Output
(in units)
Labor
costs
Overhead
costs
Material
costs
Total
costs
1
30,000
$2,880
$4,320
$2,700
$9,900
2
33,600
$3,360
$5,040
$2,820
$11,240
3
32,200
$3,360
$5,040
$2,760
$11,160
4
35,400
$3,840
$5,760
$2,880
$12,480
MFP
$
productivity
Week
Output
(in units)
Labor
costs
Overhead
costs
Material
costs
Total
costs
MFP
1
30,000
$2,880
$4,320
$2,700
$9,900
3.03
2
33,600
$3,360
$5,040
$2,820
$11,240
2.99
3
32,200
$3,360
$5,040
$2,760
$11,160
2.89
4
35,400
$3,840
$5,760
$2,880
$12,480
2.84
$
productivity
Week
Output
(in units)
Labor
costs
Overhead
costs
Material
costs
Total
costs
MFP
$
productivity
1
30,000
$2,880
$4,320
$2,700
$9,900
3.03
$424.20
2
33,600
$3,360
$5,040
$2,820
$11,240
2.99
$418.60
3
32,200
$3,360
$5,040
$2,760
$11,160
2.89
$404.60
4
35,400
$3,840
$5,760
$2,880
$12,480
2.84
$397.60
Productivity
• Rate of productivity growth (RPG)
– ((𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 − 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦)
÷ 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 ) x 100
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
Alternatives
Low
Moderate
High
Small facility
$10
$10
$10
7
12
12
(4)
2
16
Medium facility
Large facility
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)
NEXT YEAR’S DEMAND
Alternatives
Low
HIGH
Do nothing
$50
$60
Expand
20
80
Subcontract
40
70
• Maximax
– 80, Expand
• Maximin
– 50, Do nothing
Decision making under uncertainty
• Problem 1
• Laplace
NEXT YEAR’S DEMAND
Alternatives
Low
HIGH
Do nothing
$50
$60
($50+$60)/2 = $55
Expand
20
80
($20+$80)/2 = $50
Subcontract
40
70
($40+$70)/2 = $55
– Now we have problem!
Decision making under uncertainty
• Problem 1
• Minimax regrets (opportunity losses)
NEXT YEAR’S DEMAND
Alternatives
Low
HIGH
Do nothing
$50
$60
Expand
20
80
Subcontract
40
70
Decision making under uncertainty
• Problem 1
• Minimax regrets
NEXT YEAR’S DEMAND
Alternatives
Low
HIGH
WORST
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
– subcontract
Decision making under risk
• Problem 2(a)
• EMV (expected profit)
NEXT YEAR’S DEMAND
Alternatives
Low P(.30)
HIGH P(.70)
Do nothing
$50
$60
Expand
20
80
Subcontract
40
70
• EMV(Do nothing): 50(.3) + 60(.7) = $57
• EMV(Expand):
20(.3) + 80(.7) = $62
• EMV(Subcontract): 40(.3) + 70(.7) = $61
Decision making under risk
• Problem 2(c)
• Expected value of perfect information (EVPI)
NEXT YEAR’S DEMAND
Alternatives
Low P(.30)
HIGH P(.70)
Do nothing
$50
$60
Expand
20
80
Subcontract
40
70
• Expected payoff under certainty (EPC)
– 50(.3) + 80(.7) = 71
• Expected payoff under risk
– PR (EMV – Expand) = 62
• EVPI = 71 – 62 = 9
Decision trees
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: 0.4 + 0.65 + 0.18 = 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: 0.6 + 0.8 + 0.17 = 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: 0.56 + 0.55 + 0.24 = 1.35
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
Problem 12, p. 176
• Assume equal probabilities
• Omit the leasing option
$700
Demand low (.50)
Lease
Build small
Demand high (.50)
1
2
$100
Expand
$500
Demand low (.50)
$40
Build large
$2,000
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
$700
Demand low (.50)
Lease
Build small
Demand high (.50)
1
2
$100
Expand
$500
Demand low (.50)
$40
Build large
$2,000
Demand high (.50)
Minimax regret
Alternatives
Low
High
Build Small
$700
$500
Build Large
$40
$2,000
Alternatives
Low
High
Build Small
$700 - $700 = $0
$2,000 - $500 = $1,500
Build Large
$700 - $40 = $660
$2,000 - $2,000 = $0