Chapters 13-15
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
Corrections on slides 6, 7, 11 2015/10/05
Marginal Analysis: Definitions
X
C(X)
TV(X)
– Activity level of an alternative
– Cost of alternative
– 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) =
d(NV)
dx
= d(TV) dx
dC
dx
TV and C
Cost and Total Value
TV
C
X1
NVmax
Xmax X2
Activity level x
(a)
MNV = d(TV)/dx – dC/dx
Marginal Net Value
Xmax
(b)
X
Activity
level
Net Value vs. Activity Level
NV = TV - C
NVmax
X
Xmax
X1
Investment
Profitable
(b)
X2
Overinvestment
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) = 1007 + 20N; dC / dN = 20
TV(N) = VT(840N – 40N2); d(TV) / dN = VT(840 –80N)
20 = VT (840 – 80Nmax)
Nmax = (840 VT – 20) / 80 VT = 10.5 – 1/(4VT )
Optimal Number of Processors
vs. Transaction Value
10
8
Nmax
6
Nmax = 10.5 – 1 /(4 VT)
4
2
0.1
0.2
0.3
0.4
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.
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
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=
$50K
= $41,792
(1.0075)24
PV ($50K, .0075, 24) =
F
PV (F, r, n) =
(1 +r)n
$50K
(1.0075)24
Present Value
- Of a future cash flow F
- At an interest rate per time period r
- Over a number of time periods n
F
PV (F, r, n) =
(1 +r)n
1
- Using the discount rate D =
1+r
n
PV (F, D, n) = FD
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 + $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 = 1/1.0075 = .9925558, PVS ($2400, 1/1.0075, 24) = $52,928
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)]
Present Value Analysis
Results
Cost of A1
Simple
Analysis
$57,600
Present Value
Analysis
$52,928
Cost of A2
$50,000
$58,208
Present Value Comparison
vs.
Interest Rate
Present value, $
60622
60 57600
58208
55972
52908
50
55640
54420
52928
51494
50000
40
0
Option A2
0.25
0.5
0.75
Interest rate per month
1.0%
Option A1
TPS Decision Problem 4
• Choose best vendor operating system
– System A – Standard OS
– System A Plus
• Better diagnostics, maintenance features
• $40K added cost
Alternative TPS Operating
System Characteristics
Alternative
Criterion
System A
System A Plus
0
$40K
2. Processor overhead
200
200
3. Multiprocessor overhead
80
80
4. Measurement capability
Poor
Good
5. Trace capability
None
Adequate
6. Diagnostics, error messages
Adequate
Good
7. Maintenance support
Marginal
Good
8. Accounting system
Adequate
Very Good
9. Usage summaries
None
Good
10. Documentation
Good
Adequate
1. Added Cost
Meta-Decision Problems
Lower
cost
More
insight
The system decision problem
Lower Cost
More Stability
The system analysis decision problem
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
TPS Operating System Figure
of Merit Calculation
System A
Criterion
System A Plus
Weight
Characteristic
Rating
Weighted
Rating
Characteristic
Rating
Weighted
Rating
1. Added Cost
30
$0
10
300
$40K
4
120
2. Processor overhead
10
200
3
30
200
3
30
3. Multiprocessor overhead
15
80
3
45
80
3
45
4. Measurement capability
7
Poor
2
14
Good
8
56
5. Trace Capability
8
None
0
0
Adequate
6
48
6. Diagnostics, error msgs
10
Adequate
6
60
Good
8
80
7. Maintenance Support
10
Marginal
4
40
Good
8
80
8. Accounting system
2
Adequate
6
12
Very good
10
20
9. Usage summaries
3
None
0
0
Good
8
24
10. Documentation
5
Good
8
40
Adequate
6
30
Total
100
541
533
Delivered System Capability
(DSC)
Figure of Merit
DSC = (SC) (DC) (AV)
• SC: System Capability = Σ Wi rij
• DC: Delivered Capacity
• AV: Availability
The DSC Figure of Merit
• Dimensionless
• Covers effectiveness only
• SC component handles many criteria
• DC, AV components apply multiplicatively
Gains from System A Plus - I
•
Reduction of $150K maintenance cost
– Maintenance Support: 20%
– Diagnostics, Error Msgs.: 10%
– Documentation (worse): -10%
($30K)
(15K)
(-15K)
$30K
– Net Cost = $650K + 40 – 30 = $660K
•
Delivered capacity increase via measurement: 5%
2400 tr/sec (1.05)
•
2520 tr/sec
Availability increase via diagnostics, error
messages, trace capability: 50% less downtime
0.95
0.975
Gains from System A Plus - II
• System Capability
Criteria
Basic TPS Functions
System A
Weight
Rating
System A Plus
Score
Rating
Score
1.0
0.950
1.0
0.950
Accounting Systems
0.95
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
TPS Comparison: Delivered
System Capability
Criterion
System A
System A Plus
System capability (SC)
0.980
0.980
Delivered capability (DC)
2400
2520
Availability (AV)
0.95
0.975
Delivered system capability
(DSC)=(SC)(DC)(AV)
2234
2408
$650K
3.44
$660K
3.65
Cost
Capability/Cost ratio
Revised TPS Weighted Sum
Analysis
System A
Criterion
System A Plus
Weight
Characteristic
Rating
Weighted
Rating
Characteristic
Rating
Weighted
Rating
1. System capability (SC)
40
0.980
9
360
0.980
9
360
2. Delivered capacity (DC)
30
2400
8
240
2520
9
270
3. Availability (AV)
30
0.950
7
210
0.975
9
270
Total
100
810
900
Comparison of Weighted Sum
and DSC Figures of Merit
Relative
advantages
Weighted sum
Delivered system capability
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 Use where DC, AV factors
will not vary widely
may vary widely