Bidirectional option contract for prepositioning of relief supplies under demand uncertainty

The demand for relief supplies after a sudden disaster is uncertain and sometimes grows rapidly. Because of the uncertainty surrounding the demand, organisations dealing in relief management usually preposition relief supplies to reduce the impact of a disaster. However, with prepositioning, organisations face both overstocking and stockout risks. To reduce these risks, we introduce a bidirectional option contract (BOC) into a two-echelon relief supply chain consisting of a supplier and a humanitarian organisation (HO). We analyse the contract from the perspective of the HO and derive closed-form expressions for the prepositioning quantity and options quantity for the HO, considering uniform and exponential demand distributions of relief supplies. The condition for supply chain coordination between the supply chain members is derived. We compare the results of BOC with the benchmark wholesale price contract (WPC) to show the superiority of BOC. Finally, sensitivity analysis is performed to investigate the impact of model parameters and to determine the conditions under which the BOC is beneficial for both the HO and the supplier.