chapters 13-15
DESCRIPTION
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. d(NV). MNV(X) =. dx. d(TV). dC. =. -. - PowerPoint PPT PresentationTRANSCRIPT
Chapters 13-15
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
Multiple Goal Decision Analysis I
Marginal Analysis: DefinitionsX – 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 alternativeNV(X) = TV(X) – C(X)
MNV(X) – Marginal net value
MNV(X) =
= -dx
d(NV)
dC
dx
d(TV)dx
X1Xmax X2
Over-investment
(b)
NV
= T
V -
C
X
NVmax
Net Value vs. Activity Level
Investment Profitable
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(880N – 40N2); d(TV) / dN = VT(880 –80N)
20 = VT (880 – 80Nmax)
Nmax = (880 VT – 20) / 80 VT = 11 – 1/(4VT )
Optimal Number of Processors vs. Transaction Value
0.1 0.2 0.3 0.4
2
4
6
8
10
Nm
ax
V T, $K
Nmax = 11 – 1 /(4 VT)
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?
X = = $41,792
$50K
PV (F, r, n) =
(1.0075)24
$50K
V (X, 24) = X (1.0075)24 = $50K
PV ($50K, .0075, 24) =
F(1 +r)n
(1.0075)24
- 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
Present Value
PV (F, r, n) = F(1 +r)n
11 + F
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) = $2400PVS ($2400, D, 2) = $2400 + $2400 DPVS ($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
Simple Analysis
Present Value Analysis
Cost of A1 $57,600 $52,928
Cost of A2 $50,000 $58,208
5760055972 55640
58208
60622
50000
52908 54420 5292851494
60
50
40
00.25 0.5 0.75 1.0%
Interest rate per month
Pre
sen
t va
lue,
$
Present Value Comparisonvs.
Interest RateOption A2
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
1. Added Cost 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
Meta-Decision Problems
Lower Cost More Stability
Lowercost
More insight
The system decision problem
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 System A Plus
Criterion 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
• Reduction of $150K maintenance cost
– Maintenance Support: 20% ($30K)
– Diagnostics, Error Msgs.: 10% (15K)
– Documentation (worse): -10% (-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 - I
Gains from System A Plus - II• System Capability
WeightSystem A
Rating Score
System A PlusRating Score
Criteria
Total
Basic TPS Functions
Accounting Systems
Usage Summaries
OS Documentation
0.95
0.01
0.01
0.03
1.0
0.6
0.0
0.8
0.950
0.006
0.000
0.024
1.0
1.0
0.8
0.4
0.950
0.010
0.008
0.012
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
Cost
Capability/Cost ratio
$650K
3.44
$660K
3.65
Revised TPS Weighted Sum Analysis
System A System A Plus
Criterion 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
Weighted sum 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