Mathematical models for real-world production planning problems with sequence-dependent set-up costs

Production Planning (PP) aims at making production decisions optimizing the Manufacturing and Supply Chain performances. Given a limited amount of manufacturing resources, raw materials, and inventory space, PP minimizes the overall manufacturing and supply chain costs while meeting service level requirements and obeying operational constraints. In this research we focus on the sequencedependent set-up costs which occur when we change a product production during manufacturing. In real-world manufacturing, this cost typically depends on both the predecessor and current production. The set-up costs are also called clean-up costs, changeover costs or start-up costs (in the literature). These costs are one important part of the production costs for many real-world production systems. The set-up costs optimization may dramatically affect the quality of the production plans in terms of machine operational efficiency, cycle time, service level and inventory turns. Finally, different levels of details are typically taken into consideration which largely affect the complexity of the resulting models. In this work, we study a real-world PP problem with sequence-dependent set-up costs and we propose different formulations with different levels of details of the operational constraints.