Over the last decades, lot-sizing problems have drawn the attention of many researchers, mainly because of their numerous applications in production, distribution and inventory management problems. In this talk, we address a three-level lot sizing and transportation problem with a distribution structure (3LSPD). We consider one production plant that produces one type of item over a discrete and finite planning horizon. The objective of the problem is to determine the optimal timing and flows of goods between the different facilities while minimizing the operational and transportation costs in the whole network. We propose 16 different MIP formulations to solve the problem and based on numerical experiments, we analyze the strengths of each formulation. These conclusions are compared and contrasted to theoretical results we could prove on the LP relaxation of each formulation.
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