Collaborative hospital supply chain network design problem under uncertainty

Since 2016, hospitals in France have met to form Territorial Hospital Groups (THGs) in order to modernize their health care system. The main challenge is to allow an efficient logistics organization to adopt the new collaborative structure of the supply chain. In our work, we approach the concept of logistics pooling as a form of collaboration between hospitals in THGs. The aim is to pool and rationalize the storage of products in warehouses and optimize their distribution to care units while reducing logistics costs (transportation, storage, workforce, etc.). Besides, due to the unavailability and the incompleteness of data in real-world situations, several parameters embedded in supply chains could be imprecise or even uncertain. In this paper, a Fuzzy chance-constrained programming approach is developed based on possibility theory to solve a network design problem in a multi-supplier, multi-warehouse, and multi-commodity supply chain. The problem is designed as a minimum-cost flow graph and a linear programming optimization model is developed considering fuzzy demand. The objective is to meet the customers’ demand and nd the best allocation of products to warehouses. Different instances were generated based on realistic data from an existing territorial hospital group, and several tests were developed to reveal the benefits of collaboration and uncertainty handling.