Economic Lot Size Formula Under VMI Program with Poisson Demand

Abstract

Nowadays, inventory management plays a crucial role in manufacturing supply chains. Vendor-managed inventory (VMI) program is a collaborative initiative that shows considerable performances in managing inventories through the supply system. In this study, we discuss the VMI initiative in a serial manufacturing supply chain when there is an uncertainty in demand and provide an approximate closed-form formula for the economic lot size. In this paper, we consider a two-echelon supply chain system consisting of a manufacturer and a retailer. Under vendor-managed inventory program with centralized decision making, the manufacturer is authorized to manage inventories of all agreed upon stock keeping units at the retailer’s location. We develop a renewal reward model for the case of Poisson demand and drive the mathematical formula of the long-run average total inventory cost of supply system under VMI program, and then, we develop a closed-form approximate for the optimal solution. Finally, a numerical experiment is run and measured to evaluate the performance of our approximation.