Continuous Review and Partial Backorder Inventory System with Controllable Lead Time and Service Level Constraint

Inventory control is important in supply chain management. A great deal of research efforts have been devoted to it over a few decades. Previous researches always assume that the lead time is an exogenously parameter, and the unmet demand is backordered. However, these assumptions may not suit to the real environment. In this paper, a mathematical model regarding inventory control is set up for a buyer who employs the continuous review policy, where both the changeable lead time and the partial backordered situation are involved. Further, the optimal inventory control approach gained by the Lagrange multiplier method, is shaped to account for the service level restriction. Impacts of the backorder rate on the continuous review policy and the inventory cost are also analyzed.