Contract design between relief organisations and private-sector vendors: A humanitarian logistics framework

•We study inventory contracts from two perspectives: the objective function and the inventory subject.•We build a framework of nine kinds of contracts to get the optimal inventory management strategy in different situations.•This framework promotes the collaboration between relief organisations and private sector entities in various humanitarian situations.•We conduct a common numerical experiment based on an investigation in China, which represents the practical situations and aims at solving practical problems. Amid increasing threats from natural disasters, the demand for relief supplies is growing quickly. As such, private-sector collaborations have been an efficient way for relief organisations to mitigate the burden of supply procurement and inventory. However, due to the complexity of disasters, such collaboration contracts are not one-size-fits-all. Based on our field investigation and literature review, we summarize two important factors, the relief organisation’s objective and inventory management, which should determine the design of the contract. Each factor has three important elements, so we can build a framework for the corresponding nine kinds of contracts and propose their models. Through a common numerical experiment, we make comparisons and further clarify their characteristics. The results of this analysis may be helpful in determining which kind of contract is most suitable to promote collaboration between relief organisations and private-sector entities in different humanitarian situations.