A Two Steps Approximation Method to Solve Vendor Managed Inventory Problems for Many Retailers with Stochastic Demands

Abstract

The purpose of this manuscript is to design a Vendor Managed Inventory (VMI) model for many retailers in a supply chain having stochastic demands to reduce the total cost of the supply chain. We first develop a VMI model for many retailers where vendor manage its inventory on a base stock policy. The resulting model is characterized by a lumpy demand at the supplier’s side. Even when information of demand from retailers are fully shared with the supplier, the model becomes untractably nonlinear that cannot be solved easily. When developing the model for many retailers, we come to realization that not only do demands behave stochastically but periods of demand actualizations are also stochastic. In addition, a simultaneous formulation for both vendor and retailers’ inventory model is rather difficult to solve because of the uncertain complexity. We propose a two-steps approximation approach to solve this non-linear problem.