A finite-horizon inventory problem with deterministic, dynamic demand and stochastic supply disruptions

We study a single-item periodic-review finite-horizon inventory system. The system has uncertainty supply and a deterministic dynamic demand structure which is generated by the Bass diffusion model.;We propose a dynamic programming algorithm with complete disruptions in which the supply uncertainty is structured by a Markov process. We demonstrate how the inventory policy is affected by the model's parameters.;We also claim that our model is more realistic than the most closely related model, by Gullu et al. (1997). Whereas Gullu et al.'s model structures supply uncertainty as a Bernoulli process, we model them as a Markov process. We also propose a dynamic programming algorithm with partial disruptions. We investigate both zero fixed ordering cost and non-zero fixed ordering cost. In the case of zero fixed ordering cost, we show that our model is more flexible than Gullu et al.'s model (1999). Our model can deal with any level of disruptions while Gullu et al.'s model is limited at 3 levels of disruptions. We show that when the supply may have partial disruptions, one should use a state dependent order-up-to level policy. In the case of non-zero fixed ordering cost, we show that it is not always true that an (s, S) policy is optimal.;Finally, we demonstrate that in a supply uncertainty scenario the complete disruption model produces a lower inventory cost than the Wagner-Whitin model.