Designing a new framework agreement in humanitarian logistics based on deprivation cost functions

In preparation for a potential disaster, it is important to have cooperative relationships in place between relief organizations and businesses. Through a suitable framework agreement (FA), relief organizations can reduce a large amount of the inventory costs and decrease the social costs (i.e., the sum of deprivation costs and logistics costs) associated with their humanitarian operations, while businesses can make more profit. Unfortunately, in China, such cooperation between local authorities and business enterprises is still far from developed, due to the lack of high-quality FA contracts. In this paper, we solve the problem by designing a new FA that has an incentive for both relief organizations and businesses to establish the partnership, leading to a win-win situation. Unlike the widely studied contracts that are based on quantity and corresponding pricing strategies for relief items, the FA designed here incentivizes the delivery time, and encourages faster delivery of relief items, which is also important in mitigating human suffering. We consider the uncertainty of disaster timing and the dynamic relationships between delivery lead times and logistics/deprivation costs, and propose a decision-making process for relief organizations and partner businesses to negotiate and sign the new FA. A case study based on real-world data from a field investigation is conducted to prove the feasibility and effectiveness of our new FA.