We study an integrated process configuration, lot-sizing, and scheduling problem, which appears in a real production environment in the packaging industry. Products are produced by alternative process configurations. The production quantities and capacity consumption depend on which process configurations are used, how long they are used for, and in which sequence. For the particular case studied here, configuration decisions are generated at the same time as lot-sizing and sequencing decisions, which involve sequence-dependent setup costs and times. Due to dependency of these decisions, the model is nonlinear. Even though a linearization technique can be applied, the problem is still difficult to solve by a mixed integer programming (MIP) solver due to its complexity. This paper aims to develop efficient solution methods to deal with this integrated production planning problem. An exact branch-and-check (B&Ch) algorithm based on a relaxed formulation and using logic-based Benders cuts is proposed to find optimal solutions. In addition, symmetry-breaking constraints are applied to strengthen the formulations. Results show that in general, the B&Ch outperforms the linearized models solved by an MIP solver. To efficiently solve large instances, an MIP-based heuristic is then proposed to find good quality solutions in shorter computing times. Although the problem studied here is based on the packaging industry, the logic of the B&Ch and the proposed heuristic can be adapted to other applications where lot-sizing must be determined simultaneously with process configuration decisions.
Published September 2018 , 27 pages