Pre-positioning of relief inventories: a multi-product newsvendor approach

Inventory pre-positioning is critical to quickly and efficiently responding to potential disasters. This paper considers a NPO (a relief agent) that requires stockpiling multiple products for responding multiple potential disaster events. By employing the multi-product newsvendor (MPNV) approach, this paper establishes a multiple relief materials' storage model that aims to minimise the expected total cost of the NPO. Our model acknowledges that the occurrence of a disaster, the demand after a disaster and the donation after a disaster are uncertain. Given the no-budget constraint, this paper shows the implicit conditions that determine the optimal solutions; for the case with a budget constraint, the paper develops a two-binary iterative approach to solve the model with a budget constraint. Numerical examples are conducted to investigate the impacts of model parameters. The paper further proposes a flexible storage policy, in which the NPO and the supplier jointly stockpile relief materials. The optimal solution of the case with the flexible stockpiling policy is also characterised. Moreover, this paper shows the policy implementation can simultaneously increase the performance of the NPO and the supplier; and both players of the supply chain prefer that the supplier solely holds all inventory.