A two-period newsvendor model for prepositioning with a post-disaster replenishment using Bayesian demand update

Humanitarian aid agencies usually resort to inventory prepositioning to mitigate the impact of disasters by sending emergency supplies to the affected area as quickly as possible. However, a lack of replenishment opportunity after a disaster can greatly hamper the effectiveness of the relief operation due to uncertainty in demand. In this paper, a prepositioning problem is formulated as a two-period newsvendor model where the response phase is divided into two periods. The model acknowledges the demand to be uncertain even after the disaster and utilises the Bayesian approach to revise the demand of the second period. Based on the revised demand, an order is placed at the beginning of the second period to be replenished instantaneously. A two-stage solution methodology is proposed to find the prepositioning quantity and post-disaster replenishment quantity, which minimise the total expected costs of relief operations. A numerical example is presented to demonstrate the solution methodology, and sensitivity analysis is performed to examine the effect of model parameters. The results highlight the indifferent characteristics shown by the replenishment quantity with the variation in model parameters.