Metaheuristics for solving economic lot scheduling problems (ELSP) using time-varying lot-sizes approach

The Economic Lot Scheduling Problem (ELSP) on a single facility (or machine) with the time-varying lot-sizes approach and with sequence-independent/sequence-dependent setup times of parts or products is studied in this paper. The objective is to minimise the long-run average inventory carrying cost and setup costs of products. While the frequency of production of a product is determined from an existing heuristic, we allow for possible changes in the heuristically computed frequencies of parts (or products) and hence attempt to reduce the total cost per cycle during the metaheuristic search process. Three metaheuristics, namely, a Genetic Algorithm (GA), a Simulated-annealing Algorithm (SA) and an Ant-Colony Algorithm (ACA) are proposed. A new crossover operator is designed and incorporated in the proposed GA. New perturbation schemes are incorporated in the proposed SA. In the proposed ACA, the initialisation and updating of pheromone intensity (or trails) are done subject to certain conditions presented in this work. The best-performing existing heuristic algorithm and the proposed algorithms for ELSP with sequence-independent setup times of products are evaluated by considering a couple of benchmark problems and by generating many problems with different number of products and comparing the solutions. In addition, we consider the case of sequence-dependent setup times and the associated setup costs. The performances of the existing algorithm and the proposed algorithms are evaluated by considering a proposed (computationally simple) lower bound on total cost per cycle with the consideration of sequence-dependent setup times and the associated setup costs of products. The computational performance analyses reveal the effectiveness of the proposed metaheuristics.