Relief item inventory planning under centralized and decentralized bilateral cooperation and uncertain transshipment quantities

Pre-positioning relief inventory ensures timely delivery of in-kind aid after a catastrophe. Tragic disasters like major earthquakes are rare and unpredictable; therefore, stockpiled items may not be used. To avoid over-stocking and reduce shortage risk, the cooperation of two humanitarian agencies in supporting each other in case of shortages is suggested in the literature. In this study, we utilize newsvendor-based quantitative models to optimize the pre-disaster stocking decisions of agencies under centralized and decentralized cooperation mechanisms. In the former, both agencies jointly determine their inventory levels to maximize their combined benefits of relief operations, whereas, in the latter, each agency establishes its stocking level in isolation via a game theoretic approach. In both systems, the two agencies agree to transship their excessive items to the other party if needed. In this regard, we investigate the situation where only a portion of the transshipped items, denoted as the reliability factor, can be received and effectively utilized at the destination due to the chaotic nature of the disaster. Considering a deterministic reliability factor, we obtain the singular optimal inventory levels in the centralized system and identify the unique Nash Equilibrium in the decentralized system. Subsequently, we formulate a two-stage stochastic program, considering a random reliability factor for both cooperation systems. The study concludes by offering a range of managerial insights. Our analyses quantify the sub-optimality resulting from decentralized decision-making across diverse parameter settings using the concept of the price of anarchy. The findings highlight that centralized cooperation becomes particularly advisable when the average demand within either agency is high, the transshipment process is secure (i.e., the reliability factor is high), and transshipment costs remain low.