1. Multiple Goal Decision Analysis I Chapters 13-15 in SEE Updated to MedFRS
Barry Boehm, USC-CSSE
CS 510, Fall 2018
Fall 2018
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2. Topics in Multiple Goal Decision Analysis I
Net value and marginal analysis
Decision rules
Example
Present value analysis
Reconciling present and future cash flows
Discounting
Figures of merit
Weighted sum
Delivered system capability
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3. Marginal Analysis: Definitions
X – Activity level of an alternative
C(X) – Cost of alternative
TV(X) – Total value of alternative
(in same units as cost)
NV(X) – Net value of alternative
NV(X) = TV(X) – C(X)
MNV(X) – Marginal net value
MNV(X) = = - dx
d(NV) dC
d(TV)
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4. Cost and Total Value TV and C Activity level x (a) TV NVmax C X1 Xmax
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5. Marginal Net Value Activity level MNV = d(TV)/dx – dC/dx (b) Xmax X
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6. Net Value vs. Activity LevelX1
Xmax X2
Over-
investment
(b)
NV = TV - C X
NVmax
Investment
Profitable
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7. Marginal Net Value Decision Rule
In the “profitable” segment
If MNV > 0, Increase activity level
If MNV < 0, Decrease activity level
If MNV = 0, Activity level is optimal
MNV = d(TV)/dx – dC/dx
For Option B, with VT = value of each TR/sec,
C(N) = N; dC / dN = 20
TV(N) = VT(840N – 40N2); d(TV) / dN = VT(840 –80N)
20 = VT (840 – 80Nmax) This sets MNV to zero.
Nmax = (840 VT – 20) / 80 VT = 10.5 – 1/(4VT )
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8. Optimal Number of Processors
vs. Transaction Value 10 8 6
Nmax = 10.5 – 1 /(4 VT)
Nmax 4 2
VT, $K
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9. MedFRS TPS Decision Problem 3
Assuming use of composite option, we will acquire 5 processors/system and run option A for 2 years
Which acquisition option should we choose: -A1: Rent processors for 2 years at $2400/Mo. -A2: Purchase processors for $100,000.
Resell them for $50,000 after 2 years.
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10. Interest Calculations
Option A2 ties up $50K for 24 months
How much would this be worth at an interest rate of .75%/month? V($50 K, 1) = $50 K (1.0075) V($50 K, 2) = $50 K (1.0075) (1.0075) … V($50 K, 24) = $50 K (1.0075)24 = $59,820
For any sum X, V(X, 24) = X(1.0075)24
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11. Present Value Calculations
What is the present value X of the $50K we will receive in 24 months?
V (X, 24) = X (1.0075)24 = $50K
X =
= $41,792
(1.0075)24
$50K
Therefore, the present value of the A2 cost = $100,000 - $41,792 = $58,208
$50K
PV ($50K, .0075, 24) =
(1.0075)24 F
PV (F, r, n) =
(1 +r)n
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12. Present Value Of a future cash flow F
At an interest rate per time period r
Over a number of time periods n
Using the discount rate D =
PV (F, D, n) = FDn F
PV (F, r, n) =
(1 +r)n 1
1 + r
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13. Present Value, Series of Cash Flows
In option A1, we pay $2400 at the beginning of each month
How much is this worth in present value? PVS ($2400, D, 1) = $2400 PVS ($2400, D, 2) = $ $2400 D PVS ($2400, D, 3) = $2400 (1 + D + D2)
PVS ($2400, D, 24) = $2400 (1 + D + … + D23) = $2400 (1 - D24) / (1 – D )
For D = 1/ = , PVS ($2400, 1/1.0075, 24) = $52,928
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14. Present Value of a Series of Cash Flows
m equal cash flows or payments P
At the beginning of each time period
Constant discount rate D
PVS (P, D, m) = P [(1-Dm)/(1-D)]
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15. Present Value Analysis Results
Simple Analysis
Present Value Analysis
Cost of A1
$57,600
$52,928
Cost of A2
$50,000
$58,208
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16. Present Value Comparison
vs.
Interest Rate
57600
55972
55640
58208
60622
50000
52908
54420
52928
51494 60 50 40
0.25
0.5
0.75
1.0%
Interest rate per month
Present value, $
Option A2
Option A1
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17. TPS Decision Problem 4 Choose best vendor operating system
System A – Standard OS
System A Plus
Better diagnostics, maintenance features
$40K added cost
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18. Alternative TPS Operating System Characteristics
Criterion
System A
System A Plus
1. Added Cost
$40K
2. Processor overhead
200
3. Multiprocessor overhead 80
4. Measurement capability
Poor
Good
5. Trace capability
None
Adequate
6. Diagnostics, error messages
7. Maintenance support
Marginal
8. Accounting system
Very Good
9. Usage summaries
10. Documentation
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19. Meta-Decision Problems
Lower cost
More insight
The system decision problem
Lower Cost
More Stability
The system analysis decision problem
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20. Weighted Sum Figure of Merit
Assign weight Wi to criterion i
Σi Wi = 1
For each option j and criterion i,
assign rating riJ (0 < rij < 10)
Compute figure of merit for each option j
Fj = Σ Wi rij
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21. TPS Operating System Figure of Merit Calculation
System A
System A Plus
Criterion
Weight
Characteristic
Rating
Weighted Rating
1. Added Cost 30 $0 10
300
$40K 4
120
2. Processor overhead
200 3
3. Multiprocessor overhead 15 80 45
4. Measurement capability 7
Poor 2 14
Good 8 56
5. Trace Capability
None
Adequate 6 48
6. Diagnostics, error msgs 60
7. Maintenance Support
Marginal 40
8. Accounting system 12
Very good 20
9. Usage summaries 24
10. Documentation 5
Total
100
541
533
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22. Delivered System Capability (DSC) Figure of Merit
DSC = (SC) (DC) (AV)
SC: System Capability = Σ Wi rij
DC: Delivered Capacity
AV: Availability
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23. The DSC Figure of Merit Dimensionless Covers effectiveness only
SC component handles many criteria
DC, AV components apply multiplicatively
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24. Gains from System A Plus - I
Reduction of $150K System A maintenance cost
– Maintenance Support: % ($30K)
– Diagnostics, Error Msgs.: 10% (15K)
– Documentation (worse): -10% (-15K)
$30K
– Net Cost = $650K + 40K – 30K = $660K
Delivered capacity increase via measurement: 5%
2400 tr/sec (1.05) tr/sec
Availability increase via diagnostics, error messages, trace capability: 50% less downtime
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25. Gains from System A Plus - II
System Capability
System A
System A Plus
Criteria
Weight
Rating
Score
Rating
Score
Basic TPS Functions
0.95
1.0
0.950
1.0
0.950
Accounting Systems
0.01
0.6
0.006
1.0
0.010
Usage Summaries
0.01
0.0
0.000
0.8
0.008
OS Documentation
0.03
0.8
0.024
0.4
0.012
Total
0.980
0.980
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26. TPS Comparison: Delivered System Capability (DSC)
Criterion
System A
System A Plus
System capability (SC)
0.980
Delivered capability (DC)
2400
2520
Availability (AV)
0.95
0.975
Delivered system capability
(DSC)=(SC)(DC)(AV)
2234
2408
Cost
Capability/Cost ratio
$650K
3.44
$660K
3.65
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27. Revised TPS Weighted Sum Analysis
System A
System A Plus
Criterion
Weight
Characteristic
Rating
Weighted Rating
1. System capability (SC) 40
0.980 9
360
2. Delivered capacity (DC) 30
2400 8
240
2520
270
3. Availability (AV)
0.950 7
210
0.975
Total
100
810
900
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28. Comparison of Weighted Sum and DSC Figures of Merit
Delivered system capability
Relative advantages
Simpler
More representative of many computer systems
Better for assessing side effects of DC, AV factors
Better for assessing wide variations in DC, AV factors
Recommendation
Use where DC, AV factors will not vary widely
Use where DC, AV factors may vary widely
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