Fuzzy Linear Programming: A Modern Tool for Decision Making

Abstract

Abstract:In this paper, the S-curve membership function methodology is used in a real life industrial problem of mix product selection. This problem occurs in the chocolate manufacturing industry whereby a decision maker, analyst and implementer play important roles in making decisions in an uncertain environment. As analysts, we try to find a solution with a higher level of satisfaction for the decision maker to make a final decision. This problem of mix product selection is considered because all the coefficients such as objective, technical and resource variables are fuzzy. This is considered as one of sufficiently large problem involving 29 constraints and 8 variables. A decision maker can identify which vagueness ( ) is suitable for achieving satisfactory optimal revenue. The decision maker can also suggest to the analyst some possible and practicable changes in fuzzy intervals for improving the satisfactory revenue. This interactive process has to go on among the analyst, the decision maker and the implementer until an optimum satisfactory solution is achieved and implemented.

An optimization model for fuzzy nonlinear programming with Beale's conditions using trapezoidal membership functions

“…The verdicts are fuzzy in maximum real-life situations, and initial attempts at the choices are essential to formulate a suitable model or cases to be analyzed. Likewise, we introduce fuzziness in our models of such situations to suggest means of processing fuzzy information [4]. In linear programming solution that satisfies both the constraints and the objective function has been named an optimum solution.…”

Fuzzy Optimization of Cost Function in Product Mix Selection Problem

“…That is to find the optimal product mix under uncertain constraints in the technical, raw material and market consideration. Furthermore, it is possible to show the relationship between the optimal cost and the corresponding membership values (Vasant et al, 2002a). According…”