Abstract
Subjective selection of weights in method of combining objective functions in a multi – objective programming problem may favour some objective functions and thus suppressing the impact of others in the overall analysis of the system. It may not be possible to generate all possible Pareto optimal solution as required in some cases. In this paper we develop a technique for selecting weights for converting a multi-objective linear programming problem into a single objective linear programming problem. The weights selected by our technique do not require interaction with the decision makers as is commonly the case. Also, we develop a technique to generate all possible Pareto optimal solutions in a multi-objective linear programming problem. Our technique is illustrated with two and three objective function problems.
Highlights
There is increasing interest in research in the area of multiobjective programming. [1] presents an alternative method based on fuzzy programming for solving multi-objective linear bi-level multi-follower programming problem in which there is no sharing of information among followers; a multiobjective programming model for selecting third – party logistics companies and suppliers in a closed-looped supply chain was proposed in [2,3] proposed a fuzzy robust programming approach to multi-objective portfolio optimization problem under uncertainty and lot more
A feasible solution to a multi-objective linear programming problem is considered to be optimal if it is better than any other feasible solution for all linear programming problems that constitute the multi-objective programming problem
In this paper we present a technique for weights determination that does not involve interaction with the decision maker while the optimization process is ongoing, and the procedure for the generation of all Pareto optimal solutions is presented
Summary
There is increasing interest in research in the area of multiobjective programming. [1] presents an alternative method based on fuzzy programming for solving multi-objective linear bi-level multi-follower programming problem in which there is no sharing of information among followers; a multiobjective programming model for selecting third – party logistics companies and suppliers in a closed-looped supply chain was proposed in [2,3] proposed a fuzzy robust programming approach to multi-objective portfolio optimization problem under uncertainty and lot more. A good but, not necessarily optimal solution to a multiobjective linear programming problem is known as efficient or non-inferior or Pareto optimal solution. A solution to a multi-objective linear programming problem is said to be efficient if it is not possible to improve some objective function values at expense of others Such solutions are infinitely many and so interest is always on generating some of them. The decision maker states his preferences before selecting weights to combine several objectives function to form single objective function. In this paper we present a technique for weights determination that does not involve interaction with the decision maker while the optimization process is ongoing, and the procedure for the generation of all Pareto optimal solutions is presented
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