Optimal inventory decisions in a multiperiod newsvendor problem with partially observed Markovian supply capacities

This paper considers a multi-period news-vendor problem with partially observed supply capacity information which evolves as a Markovian Process. The supply capacity is fully observed by the buyer when the capacity is smaller than buyer’s ordering quantity. With a dynamic programming formulation, we prove the existence of a unique optimal ordering policy. In a two-state Markovian capacity case, we further demonstrate that the buyer orders more than required to reveal supply capacity. We also provide a numerical example to demonstrate the characterization of the optimal policy. Note to Practitioners— Supplier management is a critical task for inventory managers, in particular, when there existing supply uncertainties. In such circumstances, inventory managers have to make inventory replenishment decisions based on their best estimation of supply conditions. Their past experiences are the basis for estimation. Note that their past experiences, to the best, only partially reveals the supply condition. This paper develops a new model in which it makes use of a partial observed supply capacity information, which is derived in the order fulfillment process, to forecast the future supply capacity. There are two possible observations of the order fulfillment: (1) if the ordering quantity is greater than the current period supply capacity, the buyer observes the value of the current period supply capacity; (2) otherwise, the buyer knows that the current period supply capacity is greater than its ordering quantity. Based on these two observations, the buyer updates the future supply capacity forecasting accordingly. Compared with traditional models, we demonstrate that making use of the partial observed information significantly reduces costs of inventory systems. However, this inventory model assumes that all the leftover inventories are salvaged at the end of each period. This assumption is applicable to perishable products. For future research, extending this model to cases where leftover inventories to be carried to the next period is the future research direction.