A heuristic based on mathematical programming for a lot-sizing and scheduling problem in mold-injection production

Abstract This paper studies a lot-sizing and scheduling problem to maximize the profit of assembled products over several periods. The setting involves a plastic injection production environment where pieces are produced using auxiliary equipment (molds) to form finished products. Each piece may be processed in a set of molds with different production rates on various machines. The production rate varies according to the piece, mold and machine assignments. The novelty lies on the problem definition, where the focus is on finished products. We developed a two-stage iterative heuristic based on mathematical programming. First the lot-size of the products is determined together with the mold-machine assignments. The second stage determines if there is a feasible schedule of the molds with no overlapping. If unsuccessful, it goes back to the first stage and restricts the number of machines that a mold can visit, until a feasible solution is found. This decomposition approach allows us to deal with a more complex environment that incorporates idle times and assembly line considerations. We show the advantages of this methodology on randomly generated instances and on data from real companies. Experimental results show that our heuristic converges to a feasible solution with few iterations, obtaining solutions that the companies find competitive both in terms of quality and running times.