Personal Computer-Aided Interactive Decision Making for Multiobjective Linear Programming Problems with Fuzzy Coefficients and Its Applications

Abstract

In this paper, we focus on multiobjective linear programming problems with fuzzy coefficients and present a personal computer-aided interactive decision making method for obtaining the satisficing solution of the decision maker (DM) on the basis of the linear programming method. The fuzzy coefficients in the description of the objective functions and the constraints, which reflect the experts’ ambiguous understanding of the nature of the coefficients in the problem-formulation process, are characterized by fuzzy numbers. The concept of (α, β)-multiobjective linear programming and (α, β)-Pareto optimality is introduced based on the α-level and β-level sets of fuzzy numbers. In our interactive decision making method, in order to generate a candidate for the satisficing solution of the DM which is also (α, β)-Pareto optimal, if the DM specifies the degree a and S of the α-level and β-level sets and the reference objective values, the minimax problem is solved by making use of the linear programming method, and the DM is supplied with the corresponding (α, β)-Pareto optimal solution together with the trade-off rates among the values of the objective functions and the degree α and β. Then by considering the current values of the objective functions, α and β as well as the trade-off rates, the DM acts on this solution by updating his/her reference objective values and/or the degree α, β. In this way the satisficing solution for the DM can be derived efficiently from among an (α, β)-Pareto optimal solution set. On the basis of the proposed method, interactive FORTRAN programs, which run on N.E.C. PC-9801 series personal computers, are developed to implement man-machine interactive procedures. An application to an optimal operation problem in a package system in automated warehouses is demonstrated together with the corresponding personal computer outputs.