Solving Two-Machine Assembly Scheduling Problems With and Without Inventory Constraints

This paper considers a scheduling problem with component availability constraints in a supply chain consisting of two manufacturing and a merge-intransit facilities. Three mixed-integer programming (MIP) models and a constraint programming (CP) model are studied, and their performance are compared in an extensive numerical study. The results show that one of the MIP models that uses time index variables is the best performer in terms of proving optimality for problems with short processing times and a small number of orders whereas the CP model outperforms the others for problems with longer processing times and/or a large number of orders. Moreover, CP model consistently finds a feasible solution in the majority of problem instances unlike any of the MIP models. These results indicate that the CP model is a good candidate for a practitioner to use in real life implementations.