The Optimization of a Revenue Function in a Fuzzy Linear Programming Model Used for Industrial Production Planning

Abstract

In this paper, the S-curve membership function methodology is used in a reallife industrial problem in which there are various products, each of which requires a certain mix of raw materials selected from a set of available raw materials. This problem occurs in the chocolate manufacturing industry where decision makers and implementers play important roles that enable successful manufacturing of the products in an uncertain environment. The analysis in this paper tries to find a solution that helps a decision maker when deciding on what to implement. This problem is considered because it can be modeled with the help of fuzzy parameters (for example, the availability of raw materials is not always certain, and so can be treated as a fuzzy parameter). With 29 constraints and 8 variables the problem here is sufficiently large for the S-curve methodology employed because this methodology is applicable to problems with as few as 1 constraint and 1 variable. A decision maker can specify which vagueness parameter α is suitable for achieving a revenue which through the analysis results in an initial solution that can be implemented. From the results of this implementation the decision maker can then suggest some possible and practicable changes in fuzzy intervals for improving the revenue. Within the framework of the analysis this interactive process has to go on between the decision maker and the implementer until an optimum solution is achieved and implemented.