Stochastic modeling of a single-vendor single-buyer supply chain with (s, S)-inventory policy

Given the relevance of stochastic modelling in supply chain analysis and the advances in queuing theory in different subject fields (such as in-plant manufacturing systems), the present paper deals with the application of a Bernoulli model to the simple but representative (and frequently cited) case of a single-vendor single-buyer supply chain with (s, S)-inventory policy, where the maximum capacity S has to be restored in the intermediate warehouse whenever the inventory position reaches or drops below the reorder point s. An analytical stochastic model is presented which considers two two sources of uncertainty, supply uncertainty and demand uncertainty. The model is analytically formulated and solved in closed-form in order to compute some significant performance measures and, consequently, support tactical decisions (such as the definition of the design parameters s and S). Then, the model setting up is discussed. Specifically, the problem of relating demand and supply probabilities to the behaviour exhibited by the buyer and (particularly) the vendor is addressed. Finally, some numerical results are provided for illustration.