Multicriterion decision making in river basin planning and development

Abstract

Five Multicriterion Decision Making (MCDM) methods, namely, ELECTRE-2, PROMETHEE-2, Analytic Hierarchy Process (AHP), Compromise Programming (CP) and EXPROM-2 are employed to select the best reservoir configuration for the case study of Chaliyar river basin, Kerala, India. Spearman rank correlation coefficient is used to assess the correlation between the ranks obtained by the above MCDM methods. Although, these methods follow different approaches, the analysis has shown that the same preference strategy is reached by all the methods. Comparative evaluation of MCDM methods revealed that Compromise Programming is best suited for the present case study.

Introduction

Design of water resources systems are generally complex in nature as it involves large number of factors which are tangible and intangible as well as qualitative and quantitative. In planning of the development of a river basin choosing the most suitable one from the different configurations of reservoirs is not an easy task. This complexity necessitates the utilisation of Multicriterion Decision Making (MCDM) methods. The chosen one could be further analysed in depth for its final implementation.

Several MCDM methods have been developed and applied to various case studies in river basin planning (Gershon and Duckstein, 1983, Ko et al., 1994, Pillai and Srinivasa Raju, 1995). The present paper deals with the river basin planning problem where eight alternative reservoir configurations are analysed to select the most suitable one with respect to six non-commensurable discrete criteria, namely, irrigation, power production, drinking water supply, environmental quality, flood protection and benefits from the project. Five different MCDM methods, i.e., ELECTRE-2 (outranking), PROMETHEE-2 (outranking), Analytic Hierarchy Process (priority), Compromise Programming (distance) and EXPROM-2 (EXtension of PROMETHEE-2 in distance based environment) are employed. Even though both ELECTRE-2 and PROMETHEE-2 are outranking in nature, they are adopted because of their different approaches. A brief description of the utilisation of the methods are discussed here. More details are available elsewhere (Srinivasa Raju, 1995).

ELECTRE-2 (ELimination and (Et) Choice Translating REality) is of outranking nature. The problem is to be so formulated as to choose the alternatives that are preferred for most of the criteria whereas they should not cause an unacceptable level of discontent for any of the criteria. These two requirements lead to the procedures where the concepts of concordance, discordance and threshold values are used from which strong and weak relationships are developed. These are then used in an iterative procedure to obtain the ranking of the alternatives (Gershon and Duckstein, 1983).

PROMETHEE-2 (Preference Ranking Organisation METHod of Enrichment Evaluation) is also of outranking nature. When two alternatives a and b are to be compared for any criterion j, they can be expressed in terms of preference function P_j(a,b) which is a function of the difference between the two alternatives a and b and type of criterion function. Brans et al. (1986) proposed six types of criterion functions i.e., usual criterion, quasi criterion, criterion with linear preference, level criterion, criterion with linear preference and indifference area and Gaussian criterion. Indifference and preference thresholds are also defined. Multicriterion preference index (weighted average of the preference functions P_j(a,b)) can be calculated from which ranking of the alternatives are obtained.

EXPROM-2 is the modified and extended version of PROMETHEE-2 where the relative performance of one alternative over the other is defined by two preference indices, one by weak preference index (based on outranking, i.e., multicriterion preference index in PROMETHEE-2) and the other by strict preference index (based on the notion of the ideal and the anti-ideal). The total preference index, i.e., summation of strict and weak (multicriterion) preference indices in the fuzzy environment gives an accurate measure of the intensity of preference of one alternative over the other for all criteria (Diakoulaki and Koumoutsos, 1991).

Analytic Hierarchy Process (AHP) is a method based on the priority theory. It is capable of breaking down a complex unstructured situation into its component parts. Arranging these parts in an hierarchical order and assigning numerical values based on subjective judgements and the relative importance on a numerical scale of 1–9, the judgements are synthesised to determine the overall priority of each alternative (Saaty and Gholamnezhad, 1982).

Compromise Programming defines the best as the one, whose point is at the least distance from an ideal point in the set of efficient solutions. The distance measure used in Compromise Programming is the family of L_p-metrics and is given as

$$\text{L}{}_{\mathrm{p}}\text{(a)=}\text{∑}\text{j=1}\text{J}\text{w}{}_{\mathrm{j}}{}^{\mathrm{p}}\text{f}{}_{\mathrm{j}}{}^{\mathrm{\ast }}\text{−f(a)}\text{M}{}_{\mathrm{j}}\text{−m}{}_{\mathrm{j}}{}^{\mathrm{p}}{}^{\mathrm{1/p}}\text{,}$$

where L_p(a) is the L_p-metric for alternative a, f(a) is the value of alternative a for criterion $\text{j,}\text{M}{}_{\mathrm{j}}$ and m_j are the maximum and minimum values of criterion j in set $\text{A,}\text{f}{}^{\mathrm{\ast }}{}_{\mathrm{j}}$ is the ideal value of criterion $\text{j,}\text{p}$ is the parameter reflecting the attitude of the decision maker. Alternative with minimum L_p-metric value is considered as the best (Gershon and Duckstein, 1983).