The Optimal Problem of Partial Backorder Inventory System with Service Level Constraint

In partial backorder inventory system, when demand is not satisfied, unmet demand would be backordered partially. Either backorder or lost sales would make the cost increase. For a buyer, it is important to decide how much inventory should be prepared. A great deal of research efforts have been devoted to it over a few decades. Previous researches always assume that the lead time is fixed parameter, and the unmet demand is backordered. However, these assumptions may not suit to the real environment. In this paper, we propose a mathematical model regarding inventory control for a buyer who employs the continuous review policy, where both the changeable lead time and the partial backordered situation are involved to help buyers make right decisions. We adopt more reasonable assume that the lead time is changeable and unmet demand is backordered partially. Furthermore, the optimal inventory level, order quantity and safe inventory gained by the Lagrange method, is shaped to account for the service level restriction. Impacts of the backorder rate and the service level on the continuous review policy and the inventory cost are also analyzed.