1 CRP 834: Decision Analysis Week Eight Notes

2 Plan Evaluation Methods Monetary-based technique Financial Investment Appraisal Cost-effective analysis Cost-benefit analysis Multicriteria technique Check-list of criteria Goals-achievement matrix Planning balance sheet analysis Concordance-Discordance Statistical Technique Correspondence analysis (principal component analysis) The information theory (entropy) Optimization techniques Multi-Objective Programming

3 Review of Cost-Benefit Analysis –Monetary-based technique –When evaluating over time, need to consider discount rate –The concept of consumer surplus

4 Cost-Benefit Analysis—Examples Case 1: The Simplest Case The planner is asked to design a project to provide 100 mgd of usable water, and there is but one feasible source. There are only two sensible designs – one with higher first costs, but lower OMR costs, and the other with lower first costs but higher OMR costs.

5 Case 1 (cont’d) Example: Economic life of structure – 50 years (with discounting) Design ADesign B First Cost$5,000,000$3,000,000 Annual OMR Cost$100,000$200,000 PV of OMR Cost 3% 6% $2,573,000 $1,576,000 $5,146,000 $3,152,000 Total PV, first Cost & OMR 3% 6% $7,573,000 $6,576,000 $8,146,000 $6,152,000

6 (Warning) Need to consider benefits and costs realized at different time. –Inflation –Risk and uncertainty on the rate of return –Internal rates of return: NB pv =(B 0 -C 0 )+ (B 1 -C 1 ) /(1+r)+ (B 2 -C 2 )/(1+r) 2 +… 0=(B 0 -C 0 )+ (B 1 -C 1 ) /(1+i)+ (B 2 -C 2 )/(1+i) 2 +… Where r is the interest rate, and i is the internal rate of return. Case 1 (cont’d)

7 Case 2: Two Potential Reservoirs (Q) How to design the project for the optimal costs and benefits? Reservoir Storage – Yield Data StorageY d mgd 10 3 acre feetRes. IRes. II Goal: To produce output of 100 mgd of usable water at least cost!

8 Case 2 (Cont’d) Reservoir-Cost Data Cost = Capital Cost + PV of OMR cost ( 50 year period, discount rate 5%) StorageCost ($10 5 ) 10 3 acre feetRes. IRes. II

9 Case 2 (Cont’d) Step 1: Estimate cost function –Ci=f(xi), where Ci = cost, xi=reservoir capacity Step 2: Estimate Production (yield) –Yi=f(xi), where yi = yield, xi=reservoir capacity Step 3: Establish Iso-Output Function of combinations of Reservoirs I and II for 100 mgd usable water Step 4: Establish Iso-Output Function of combinations of Reservoirs I and II Step 5: Find the least cost combination of reservoirs using the point of tangency

10 Case 2 (Cont’d) Iso-Output Function of combinations of Reservoirs I and II Combinations of Reservoirs I and II that will provide 100 mgd of usable water Res. IRes. IITotal Storage 10 3 acre feet Output mgd Storage 10 3 acre feet Output mgd Output mgd Iso-Cost Function of combinations of Reservoirs I and II Combinations of Reservoirs I and II with total cost of $ 5.5 million. Res. IRes. IITotal Capacity 10 3 acre feet Cost $ M Capacity 10 3 acre feet Cost $ M Cost $ M

11 Case 2 (Cont’d) Iso-output curve =100 mgd Iso-cost curve = $ 5.5 M Least cost combination is at tangency of two curves: Res. I =50 *10 3 acre feet –$ 4.5 M Res. I =12 *10 3 acre feet --$ 1.5 M

12 Case 3: Two Reservoirs without specifying fixed water supply Res. II - Storage Capacity 10 3 acre Res. II - Storage Capacity 10 3 acre Scale line 125 mgd 75 mgd 50 mgd 150 mgd 100 mgd 1. Points of tangency

13 Case 4: The optimal yield at a minimum cost with budget constraint Capital Cost Total Cost Gross Benefit PV Costs and Benefits ($ M) 3 10 MC=MB Scale of output at which slopes of benefit and total cost functions are equal. Maximize NB = B(y) - C(y) Subject to: K(y) < B (Budget Constraint)

14 Multicriteria - Basic Problem Definition: a multicrtieria decision problem is a situation in which, having defined a set of actions (A) and a consistent family (F) of criteria on A, one wishes –to determine a subset of actions considered to be the best with respect to F –to divide A into subsets according to some norms (sorting problems) –to rank the actions of A from best to worst (ranking problems)

15 Balance Sheet of Project Evaluation Can be viewed as a particular application of the social cost-benefit approach to evaluation Developed by Lichfield and widely used in England Considers all benefits and all costs with respect to all community goals in one enumeration Presents a complete set of social accounts, with respect to different goals, and for consumers and producers The costs and benefits are recorded as capital (once for all) items or annual (continuing) items. Types of evaluation considered: monetary, quantitative but non-monetary, intangible, and time.

16 Check List Criteria Ranks appropriate alternative proposals on an ordinal basis in relation to a number of specific criteria. Widely used by professional land-use planners

17 Goals-Achievement Matrix Developed by Hill (1965) –M Hill A Goals-Achievement Matrix for Evaluating Alternative Plans. Application to Transportation Plans. Journal of the American Institute of Planners, Vol. 34, No. 1, This method attempts to determine the extent to which alternative plans will achieve a predetermined set of goals or objectives Costs and benefits are always defined in terms of achievement. –Benefits represent progress toward the defined objectives, while costs represent retrogression from defined objectives. –The basic difference between PBSA and GAM is that GAM only considers costs and benefits with reference to well stated objectives, and to well defined incidence groups.

18 Concordance-Discordance analysis It consists of a pair-wise comparisons based on calculated indicators of concordance or discordance. The concordance index reflects the relative dominance of a certain competing plan, and the discordance index shows the degree to which the outcomes of a certain plan are worse than the outcomes of a competing plan.

19 Concordance-Discordance analysis

20 Concordance-Discordance analysis—example

21 Multi Objective Programming (MOP) Basic Concepts and Definition of MOP Non-Dominated Solutions Generating/Incorporating Methods –Weight Method –Constraint method MOP under uncertainty

22 Why MOP? Multiple decision makers Multiple evaluating criteria Wider range of alternatives  More realistic analysis of problems * In fact, any optimization is (or should be) multiobjective!!!!

23 MOP Formulation (Vector Optimization Problem) Aims to find a vector satisfying: Where Z(x)= p-dimensional objective function x= feasible region in decision space