An application of mathematical programming to a real case of the unrelated parallel machine problem

Mathematical programming techniques are used in a tool developed to solve a real unrelated parallel machine problem in a bottle closures manufacturing plant. The tool is able to define the production process planning for a scheduling horizon of up to one month while satisfying all relevant constraints. The planning problem is a multi-objective one of minimizing production completion times, overproduction and machine idle time. Due to the problem’s complexity, the approach adopted for obtaining good solutions in reasonable execution times is based on dividing it into three subproblems or stages, each solved by a different MILP model. In the first stage, the model performs a lexicographic minimization to assign closure injection molds to the plant’s machines; in the second stage, the model corrects the machine stoppage times for mold changes; and in the third stage, the model determines the assignment of different colors to the closures or its parts produced with a given mold. Results are presented for instances of up to 100 jobs, showing how different characteristics of the problem influence the performance of the proposed solution approach. A comparison is also presented between our model’s result and the manual scheduling carried out by the factory staff for a real instance, demonstrating that our method enabled significant enhancements in the aforementioned objectives.