MULTIOBJECTIVE PROGRAMMING AND ITS APPLICATION TO A WATER RESOURCES SYSTEM

Abstract

The problem is one of multiobjective analysis and programming and its potential as a decision aiding technique in actual decision making problems with an emphasis on how the multiobjective approaches relate to the decision problems in water resources systems where multiple decision makers (DMs) are involved. Multiobjective analysis is a conceptually simple extension of single objective optimization where the problems are characterized by multiple conflicting objectives. Due to the conflicting nature of the objectives, it is difficult to simultaneously optimize all and hence the concept of optimality in single objective optimization is replaced by that of efficiency in multiobjective optimization. A number of efficient set generating techniques have been developed in literature. But the methods of its contraction to the best compromise or satisficing solution, derived from the decision makers' subjective preferences, are of importance. However, attainment of a compromise is complicated by the presence of a group of decision makers reluctant to compromise on their individual aspiration levels and thus a need arises to have an efficient interactive programming method which can lead to a sensible group compromise among the decision making group by providing them better insight into the problem. Considering the importance of group decision making in real-world multiobjective decision problems and the lack of multiple-decision-maker methods, we propose an Interactive Group Compromise Method. It is a result of the comparative study of two interactive programming approaches on the following : preference II information, learning effect or trade-off information in objective space,number of auxiliary scalar optimization problems, backtracking or ability to return to previously obtained solutions and the applicability in groups of decision makers. The proposed algorithm tries to induce a group compromise in an objective manner with a formalized technique for aggregating the subjective preferences on the individual satisfactory pareto levels of the decision makers into a preference of the whole group in the form of a common set of weights computed by a pairwise-comparisons method. As the group solution results from the individual best compromise solutions, it is readily acceptable to the decision making group. Interactive methods, are better accepted in practice as the decision makers get an opportunity to gain a greater understanding of the problem through an interaction process and, thus, are able to provide better preferences on the objective levels as the solution progresses. In the second part of the thesis we consider a water resource system and the inherent multiobjective nature of problems associated with the operation and management of multiple units to serve multiple purposes. A number of models is developed for the water resources system of Sardar Sarovar (Narmada) project (SSP) for its subsystems of hydrology, reservoir and the irrigation system served by the reservoir. These models and the results are based on the data on various system variables and parameters collected from the project authorities and are suitable for the operation and management of the respective systems. Although an , extensive amount of data has been made available,certain temporal deficiencies in the database are made up by statistical III techniques and some useful conclusions have been drawn utilizing the known and suggested approaches for data generation. A two-step disaggregation model has been developed for both spatial as well as temporal disaggregation of hydrologic traces of historical streamflow data. The disaggregated monthly streamflow traces are used for simulating reservoir operation in an implicit stochastic model with the objectives of maximizing reservoir yield and supply reliability levels for different water users. The synthetically generated traces are also used as input in a model of the irrigation system that maximizes the net benefits from total cropped area (irrigated as well as unirrigated) in the command and also the irrigated cropped area in the command. Due to the lack of temporal data on the crop patterns and the net irrigation requirements for each region,, the spatial (regional) data has been used for the development of alternative objective functions of yield and irrigated area via the statistical technique of Factor Analysis. The model takes care of the different regional and . agro-climatic characteristics that govern the yield and crop pattern in each region. Environmental impact of the project has been analyzed by the matrix display technique giving cardinal values to the relative magnitude and importance of the project activities on the physical, biological and human environment. The socio-cultural impact of the projedt has been evaluated using the limited data for Harsud town in MP which is representative of any other town coming under submergence in Gujarat due to SSP. The model computes the desirability indices for some major issues of importance to the society and Government that are weighed by a group of four IV decision makers to produce an overall impact index for the project. The pairwise-comparisons method has been used to decide group compromise weights and the resultant overall, indices are compared with the ones computed by each DM using his individual set of weights, i.e., the weights reflecting compromise among issues by each single DM. This is an attempt at an objective evaluation of the rather subjective issues that are difficult to quantify otherwise. Finally, an integrated multiobjective model of the system is developed and presented with its objective functions and constraints. The reasons for not applying the model to the real set up of SSP have been highlighted with some suggestions on the possible application of the model with the necessary data inputs and the probable model solutions with the appropriate interactive solution methodologies and a very important element, i.e., the involvement of real decision makers .in the decision making process.