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 items produced are transported to warehouses and then to retailers using direct shipments. Each retailer is linked to a unique warehouse and there are no transfers between warehouses nor between retailers. The objective is to minimize the sum of the fixed production and ordering costs and of the unit variable inventory holding costs. We compare 12 different MIP formulations to solve the problem without production nor transportation capacities. All these formulations are adapted from the MIP formulations proposed in the One-Warehouse Multi-Retailer literature, and most of the formulations proposed are newly introduced in the context of the 3LSPD. We run experiments on both a balanced and an unbalanced network (in the balanced network each warehouse serves the same number of retailers whereas in the unbalanced network 20% of the warehouses serve 80% of the retailers). Our results indicate that the richer formulations are not necessarily the best ones and that the unbalanced instances are harder to solve.
Published August 2017 , 53 pages