An integrated location-inventory-transportation problem under demand uncertainty

Motivated by a real-world application at a large international pharmaceutical company, we address a multi-period integrated location-inventory-transportation problem under demand uncertainty. The supply chain network in this problem comprises multiple plants, distribution centers (DCs), and customers. The decision-making process involves simultaneously determining the facility locations, inventory planning, and transportation volumes. Apart from the computational complexity resulting from this integration, other practical challenges arise from the fact that the planner must determine inventory policies that account for safety stock consolidation, while transportation costs are charged based on volume-based piecewise-linear costs. To address these challenges, we propose both an exact and an approximate solution framework. The exact approach relies on a logic-based Benders decomposition (LBBD) framework enhanced with a piecewise-linear lower-bound function and efficient logic cuts. To improve scalability, we also develop an approximate model using a piecewise-linear approximation for safety stock computation. Finally, using the instances derived from real-world data, we empirically demonstrate the benefits of the integrated model, which yields up to 9% of potential cost savings.