Multiple Goal Decision Analysis I 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 – 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)

Cost and Total Value TV and C Activity level x (a) TV NVmax C X1 Xmax

Marginal Net Value (b) MNV = d(TV)/dx – dC/dx Activity level Xmax X

Net Value vs. Activity Level X1 Xmax X2 Over- investment (b) NV = TV - C X NVmax 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(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 6 Nmax = 10.5 – 1 /(4 VT) Nmax 4 2 0.1 0.2 0.3 0.4 VT, $K

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 $50K X = = $41,792 (1.0075)24 $50K PV ($50K, .0075, 24) = (1.0075)24 F PV (F, r, n) = (1 +r)n

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

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 Simple Analysis Present Value Analysis Cost of A1 $57,600 $52,928 Cost of A2 $50,000 $58,208

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

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 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

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 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

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% ($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 - 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

TPS Comparison: Delivered System Capability 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

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

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