On the Economic Lot Scheduling Problem with Fuzzy Demands

In this paper, we investigate the economic lot scheduling problem (ELSP) with fuzzy demands. We assume that the demand for each product i can be approximated using some triangular membership functions. In this study, we solve the fuzzy ELSP using two basic solution approaches, namely, the Independent Solution (IS) and the Common Cycle (CC) approach. For both approaches, we derive the optimal fuzzy replenishment cycles and secure closed-form formula for their crisp figures in fuzzy sense, respectively. Also, we derive the conditions that assert the CC approach to secure the optimal solution for the fuzzy ELSP in many realistic situations. For the cases that deviate from those optimal-situations, we give an upper bound for the maximum error of the solution of the CC approach from optimality. A 10-product example demonstrates how to secure the solutions for the IS and the CC approach for the fuzzy ELSP, and illustrates the error bound of the CC approach. Keywords⎯Inventory, Economic lot size scheduling, Fuzzy sets, Fuzzy replenishment cycle, Sensitivity analysis

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