Robust multi-period blood inventory routing under multiple uncertainties

We study a multi-period blood inventory routing problem that integrates production, inventory, and distribution decisions under uncertainties in demand, donation supply, and travel times, all while accounting for the limited shelf life of blood products. Our model captures transportation efficiency through a disutility measure based on vehicles’ arrival times at hospitals, and addresses supply–demand imbalances by allowing selective rejection of service requests at a high penalty cost. We formulate a robust optimization model that simultaneously determines production quantities, inventory levels, hospital service selections, and vehicle routing for each period. The objective is to minimize the total cost over the planning horizon, which includes worst-case inventory holding, wastage, and transportation costs, unserved demand penalties, and overall transportation disutility. To obtain an exact solution, we propose an integrated algorithm within the L-shaped framework that combines Benders decomposition with a branch-and-price-and-cut (BPC) scheme. This approach decomposes the robust model into a master problem and period-specific subproblems. For a given master solution, we first use constraint programming to verify the feasibility of the subproblems, and then, if feasible, solve them with a tailored BPC algorithm to generate Benders cuts that eliminate suboptimal master solutions. Extensive numerical experiments, including a case study at the Blood Center in Chongqing, demonstrate the effectiveness of our approach. Our analysis quantifies the benefits of incorporating uncertainty and robustness while providing managerial insights through a systematic evaluation of various parameters.