Fuzzy Genetic Approach to Economic Lot – Size Scheduling Problem

The aim of this paper is to consider formulation of Economic Lot size Scheduling Problem (ELSP) in fuzzy environment with fuzzy inventory costs and objective goal. A Genetic Algorithm (GA) is used to solve the problem in the sense that it is computationally simple, yet powerful in its search for improvement. This approach is defined as Fuzzy Genetic Approach (FGA). The ELSP is a problem of scheduling the production of several different items over the same facility on a repetitive manner. The facility is such that only one item can be produced at a time. The ELSP formulation in-turn is considered under the Basic Period (BP) approach with the cycle time, Ti, of each item modified and expressed as a real multiple ki of a fundamental cycle T. As the typical inventory analysis in the real world situations is sensitive to reasonable errors in the measurement of relevant inventory costs, the inventory costs are assumed to be vague and imprecise in this paper. The objective of minimizing the total inventory cost is also imprecise in nature. The impreciseness in these variables has been represented by fuzzy linear membership functions. The bench mark problem of Bomberger’s ELSP has been worked out to highlight the method, and the results are compared with those of corresponding crisp model results. The results indicate that the FGA gives good results and works better even for higher utilization levels of the ELSP.