Multistage adaptive distributionally robust optimization for the medical supplies distribution problem with uncertain demand in humanitarian aid

Production, inventory, distribution, and dispensing of relief resources are critical operational functions in humanitarian aid. To design an efficient humanitarian relief network, it is beneficial to study these operational functions in an integrated way. Accounting for the demand uncertainty of medical supplies, we propose a multistage adaptive distributionally robust model for the medical supplies distribution network design that considers simultaneously the issues of production, inventory, distribution and dispensing of medical resources, as well as the life-loss due to the delays in treatment. The objective is to dynamically match the supply and demand of medical supplies so as to minimize the total cost consisting of the production cost, holding cost, dispensing cost, and life-loss cost related to the unmet demand. We also introduce a safety-stock and production capacity model to efficiently predetermine the initial supply of medical supplies and maximum available production abilities under the given demand information. To obtain tractable formulations, we approximate the developed models using an enhanced linear decision rule (ELDR) and a simplified ELDR (SELDR), respectively. Using a set of real-world COVID-19 data, we show that (i) both the ELDR and SELDR can yield feasible solutions extremely close to the optimal solution of the multistage adaptive distributionally robust model, whereas the SELDR is about one order of magnitude faster than the ELDR; and (ii) accounting for the safety-stock and production capacity model yields significant improvements of the obtained solution, which can also inform the decision-maker about at least how many initial supply of vaccines and the maximum available production abilities should be set to counter the risk of demand uncertainty. We also analyze the impact of some model parameters to gain managerial implications.