Prepositioning model of relief supplies based on an option contract considering human suffering

Insufficient prepositioning of relief supplies before a disaster and inefficient allocation after it are two major causes of post-disaster shortages. Such shortages can impose substantial suffering on disaster-affected populations, particularly when critical supplies are unavailable. Therefore, in addition to logistics costs, governments should pay attention to human suffering when designing relief supply systems. However, limited research has examined how human suffering affects prepositioning and supply strategies of relief supplies. To address this gap, this study develops a model grounded in option contracts for the prepositioning of relief supplies that explicitly incorporates human suffering. We derive the respective optimum strategies for the two contracting parties (the public authority and the private supplier), and further characterize the superiority conditions of the contract prepositioning model over the government‑only reserve model. Furthermore, analytical results and numerical examples are used to examine how key parameters affect the optimal decisions of both players, together with the corresponding social cost borne by the government and profit earned by the supplier. The results show that the pre-paid fee for emergency purchases can be set within a flexible range such that the minimum requirements of both parties can be satisfied. Finally, sensitivity analyses of several key parameters further provide managerial insights into government-supplier contractual cooperation, supplier selection, and pricing strategies. It shows that the model of relief supplies prepositioning under an option contract is more closely aligned with the people-centered principles of emergency response in China.