Optimal Policies for Inventory Systems with Separate Delivery-Request and Order-Quantity Decisions

Abstract

Motivated by logistics practices, we consider a retailer that replenishes its inventory by making a delivery request without specifying a quantity, then deciding the quantity when the delivery vehicle arrives after one period. A fixed cost is incurred whenever a delivery request is made, regardless of the quantity ordered later. The new feature of this research relative to previous work is the separation of the delivery request and the quantity decision, or the postponement of ordering until one-period demand information is observed. Due to such separation, both the state space and the action space must be augmented in the model. We show that the optimal policy for delivery requests is of a threshold type: A delivery request is made if and only if the inventory on hand is below a threshold. The optimal decision on ordering is more complex, and there might be multiple order-up-to levels. Our numerical studies show, nonetheless, that the cost of an ordering policy that considers (at most) two order-up-to levels is close to the minimal when the planning horizon is not too short. We also identify conditions under which a base-stock policy is optimal for ordering. To understand the effects of ordering postponement, we compare our model with the traditional model in which the two decisions must be made at the same time. We show that postponement leads not only to a lower cost, but also a higher threshold for making delivery requests.

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