Multi-product Lot-Sizing Problem with Remanufacturing, Lost Sales and Sequence-Dependent Changeover Cost

This work studies a lot-sizing problem motivated by a textile remanufacturing company in Chile. In particular, we investigate a multi-product lot-sizing with remanufacturing, lost sales, and sequence-dependent changeover costs. The problem is first formulated as a mixed-integer linear program. Then, we adapted a known family of valid inequalities and proposed a new exponential family of valid inequalities taking advantage of the problem structure. We use them in a branch-and-cut algorithm to solve the problem. The preliminary numerical results show the proposed inequalities' usefulness in strengthening the proposed formulation's linear relaxation and show that the method outperforms the generic branch-and-cut algorithm embedded in a stand-alone mathematical solver.