Inventory control with an order-time constraint: optimality, uniqueness and significance

Inventory control with an order-time constraint: optimality, uniqueness and significance

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Article ID: iaor20108923
Volume: 181
Issue: 1
Start Page Number: 603
End Page Number: 640
Publication Date: Dec 2010
Journal: Annals of Operations Research
Authors: , ,
Keywords: supply & supply chains
Abstract:

This paper analyzes a stochastic inventory problem with an order-time constraint that restricts the times at which a manufacturer places new orders to a supplier. This constraint stems from the limited upstream capacity in a supply chain, such as production capacity at a supplier or transportation capacity between a supplier and a manufacturer. Consideration of limited upstream capacity extends the classical inventory literature that unrealistically assumes infinite supplier/transporter capacity. But this consideration increases the complexity of the problem. We study the constraint under a Poisson demand process and allow for a fixed ordering cost. In presence of the constraint, we establish the optimality of an (s,S) policy under both the discounted and average cost objectives. Under the average cost objective, we show the uniqueness of the order-up-to level S. We numerically compare our model with the classical unconstrained model. We report significant savings in costs that can be achieved by using our model when the order time is constrained.

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