We analyze the classical inventory model with backordering, where the inventory position is controlled by an order level, order quantity policy. The cost for a backorder contains a fixed and a time-proportional component. Demand can be driven by any discrete process. Order lead times may be stochastic and orders are allowed to cross. The optimality condition for the order-level, given some predetermined order quantity, is derived using an easy and insightful marginal cost analysis. It is further shown how this condition can easily be (approximately) rewritten in well-known forms for special cases.

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Keywords inventory control, optimization, stochastic
Persistent URL dx.doi.org/10.1016/j.ijpe.2008.01.009, hdl.handle.net/1765/15482
Citation
Teunter, R.H., & Dekker, R.. (2008). An easy derivation of the order level optimality condition for inventory systems with backordering. International Journal of Production Economics, 114(1), 201–204. doi:10.1016/j.ijpe.2008.01.009