Simultaneous scheduling and lot-sizing with earliness/tardiness penalties

Abstract

The problem investigated in this paper is one of the simultaneous lot-sizing and scheduling problems with earliness/tardiness penalties along with the sequence-dependent setup time and cost. Minimising earliness and tardiness is of interest both in just-in-time production systems and in make-to-order ones. A mathematical model is presented similar to the travelling salesman problem. The problem objective is to determine the production lot-size and their schedules. In spite of its wide applications, this problem has not yet been reported in the literature. To solve the problem, two meta-heuristic algorithms: tabu search and ant colony system are presented. The efficiencies of the algorithms are investigated for different sets of problems. The results show that each of the ant colony system and the tabu search obtained optimal solutions for 196 and 203 problems, respectively, out of among the 333 problem instances. Despite the differences between these two methods, neither can be statistically preferred.