A genetic algorithm to solve the production lot-sizing problem with capacity adjustment

Abstract

When dynamic production capacity is considered in production lot-sizing plans, it becomes very challenging to efficiently determine the optimal production plan. Many papers apply “at most one fractional production period” to develop efficient algorithms, but those algorithms are still time consuming. In this paper, in a special situation where costs are non-speculative, we provide a novel proposal based on “at least one balance period”, in which the products made in this period not only satisfy the demands in this period but also backlogged demands and some demands after this period, to obtain an efficient algorithm. This algorithm complexity is one level lower than the algorithm without non-speculative cost assumptions in the literature regarding the number of periods in their time complexity function. Then, in a general situation, we propose a combination of two complementary algorithms as an efficient heuristic method. Moreover, in the literature, the estimation of computation time complexity in searching for the optimal production plan considers only the number of capacity levels and production periods on theoretical view. However, with numerical experiments, we observe that demand variation could also have significant effects on the computation time in practice.