A decomposition approach for the piece–mold–machine manufacturing problem

This study addresses a real manufacturing process of pieces that are produced with molds that are mounted on machines. The characteristics of the system include setup times between jobs, dedicated parallel machines, dedicated molds, and a different production rate for each piece–mold pair. There is a demand for each type of piece, and when the company fails to meet this demand, it is often forced to buy pieces from other companies to avoid loss of customers. We describe the system with a new integer quadratically constrained programming model. The proposed formulation improves others in the literature as we do not force a mold to be mounted on a single machine, which is a more realistic description of the production process itself. To solve the problem we decompose the formulation into two subproblems: one that solves the lot‐sizing of the products and another one that verifies if there is a feasible schedule for the solution of the first subproblem. This methodology is empirically tested, demonstrating its effectiveness on real size instances. Moreover, it reveals that the counterintuitive case where a mold visits more than one machine happens more often than expected.