A genetic algorithm for solving a fuzzy economic lot-size scheduling problem

This paper presents a fuzzy extension of the economic lot-size scheduling problem (ELSP) for fuzzy demands, since perturbations often occur in products demand in the real world. The ELSP is formulated via the extended basic period (EBP) approach and power-of-two policy with the demands as “approximate di0” in triangular membership function. The resulting problem thus consists of a fuzzy total cost function, fuzzy feasibility constraints and a fuzzy continuous variable (the basic period) in addition to a set of crisp binary variables corresponding to the cycle times and starts of the products' schedule. Therefore, membership functions for the fuzzy total cost function and constraints can be figured out, from which the optimal fuzzy basic period and cycle times can be determined in addition to the compromised crisp values in fuzzy sense. Also, a genetic algorithm governed by the fuzzy total cost function and fuzzy feasibility constraints is designed and assists the ELSP in search for the optimal or near-optimal solution of the binary variables. This formulation is tested and illustrated on several ELSPs with varying levels of machine utilization and products demand perturbations. The results obtained are also analyzed with the lower bound generated by the independent solution approach to the ELSPs.