|
Motivated by practices in fixed-route delivery logistics, we consider a firm who replenishes its inventory by making a delivery request without specifying the 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 (e.g., Scarf 1960 and Porteus 1971) is the separation of the delivery request and the quantity decision, or the postponement of quantity decision 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, which makes the problem technically challenging and requires non-standard tools. 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 quantity is more complex and there might be multiple order-up-to levels. Our numerical studies show, however, that the cost of an ordering policy that considers only two order-up-to levels is close to the minimal, especially when the planning horizon is long.
|