Pre-positioning of relief inventories for non-profit organizations: a newsvendor approach

Developing an efficient policy to determine the inventory a non-profit organization (NPO) should stockpile to respond to potential disasters plays a vital role in humanitarian relief. Incorporating social donation and emergency spot purchasing, this paper develops a (generalized) two-stage delivery process model to characterize relief materials’ delivery after a disaster. We propose an analytical model that aims to minimize the total costs when all demands incurred by an unexpected disaster need to be fully satisfied. Moreover, we determine that the optimal solution uniquely exists and characterize the effects of key parameters. Last, this paper also develops a risk-sharing scheme, in which the NPO and the supplier jointly stockpile relief materials. Under some mild conditions, we show that implementing the scheme could increase the storage quantity and decrease the total costs simultaneously. Several numerical examples are employed to validate the model, as well as the value of the proposed risk-sharing scheme.