The healthcare supply location-inventory-routing problem: A robust approach

Motivated by a real-world healthcare supply case of a medical implant company, this paper studies a supply network configuration problem that integrates warehouse selections for vendor managed inventory (VMI), inventory policy, and delivery routing optimization together. The problem is a variant of the classic location-inventory-routing problem (LIRP) with both deterministic demand and uncertain demand, where multi-product, multi-period, multi-type delivery, delivery time limit and VMI are considered. Two types of delivery are used: one is the scheduled bulk delivery to the VMI warehouses and the other is direct shipping for hospitals. To address the problem, first, a deterministic MILP model is presented for the integrated LIRP. Then, to deal with the uncertainty in demand, we propose a robust optimization model and transform it into a tractable linear equivalent formulation. Further, considering the effect of COVID-19 pandemic on the demand and delivery time, a new robust model is proposed to account for this special situation. Numerical experiments are conducted to verify the advantage of the proposed robust optimization models. The sensitivity analysis provides some interesting managerial insights, and a real-world case of medical implant supply configuration with 78 hospitals is solved.