The product-mold-machine manufacturing problem

This paper introduces the product-mold-machine manufacturing problem, which is related to the manufacturing process of tires, plastics, ceramics, and glass. Each product has its own shape and mechanical properties obtained from processing a specific mold on a machine. Each machine can process a set of molds at the same time and, hence, the processing time on a machine depends on the longest processing time among the set of molds on the machine. The objective is to find a production plan that minimizes the total number of periods needed to meet the demand of each product, considering a limited number of machines, molds, changeover times, and incompatibilities constraints. We provide a mixed integer linear programming model for the problem and propose two constructive heuristics of polynomial-time, which provide upper bounds on the optimal value and easy-to-implement feasible solutions. Numerical experiments carried out over instances based on real data show the effectiveness of the proposed approaches.