A dynamic two-segment partial backorder control of (r,Q) inventory system
Inventory management involves determination of shortage policy. It specifies the conditions for losing or backordering a demand. Alternative policies include pure backorder, pure lost sales, and partial backorder (using a single backorder control limit). When the backorder-cost is time dependent it makes sense to modify the backorder-limit over time. Thus, a new form of partial backorder policy (PB2) with two-segment backorder control limits is introduced. The traditional policies mentioned above, are special cases of PB2. Hence, we provide a unified framework for studying different policies that deal with shortage. The PB2 problem is formulated and solved as a discrete time, stochastic constrained control problem. Its performance is numerically compared with the simpler alternative policies. In some cases its cost savings, versus the best of PB and PL, exceeds 15%, and 7% versus a single backorder limit policy. The economical advantage is significant over a wide range of the problem parameters. This paper develops an expanded framework for modeling shortages in inventory management. It recognizes that optimal backordering strategy may change over time during an out-of-stock period. The paper is motivated by experience in the chemical industry in which, the cost of backordering is highly time related. Inventory managers, in this industry, consider to lose sales initially (once they run out of stock) and begin to backorder demand later as they approach the replenishment time. A two-segment partial backorder (r,Q) model is introduced and solved. Pure backorder (PB), pure lost sales (PL), and partial backorder (using a single backorder limit), are all special cases of the proposed model. The problem is formulated and solved as a discrete time, stochastic constrained control problem. Its performance is numerically compared with the simpler alternative policies. In some cases its cost savings, versus the best of PB and PL, exceeds 15%, and 7% versus a single backorder limit policy. The economical advantage is significant over a wide range of the problem parameters. The partial backorder policy we propose is not only different from those in the literature, but it provides new control flexibility.
partial backorder backorder inventory lost sales continuous review stochastic demand