Modeling and solving a closed-loop scheduling problem with two types of setups

Production systems with closed-loop facilities must deal with the problem of sequencing batches in consecutive loops. This article studies a problem encountered in a production facility in which plastic parts of several shapes must be painted with different colors to satisfy the demand given by a set of production orders. The shapes and the colors produce a dual-setup problem that to the best of our knowledge has not been considered in the literature. The problem is formulated as a mixed-integer program and the limitations of this approach as a viable solution method are discussed. Two alternative solution approaches are described that are heuristic in nature: one specialized procedure developed from scratch and the other one built in the framework of commercial software. The presented computational experiments were designed to assess the advantages and disadvantages of both approaches.