Ordering policies for the cyclical replenishment problem given leadtime-dependent discounts

This paper addresses a problem encountered by retailers who experience cyclical replenishment. Frequently these retailers are provided incentives for placing orders before the end of a cycle and they have to ‘wrestle’ with the questions of when to order, how many times to order, and how many units to order. The complexity of this problem arises from having to balance the reduction in unit costs with the increases in ordering costs, and in some cases deal with storage and shortage costs. It is argued that the decrease in unit cost can be directly related to the enhancement of manufacturing efficiency due to longer production leadtimes, while the increase in storage and shortage costs is a result of the increase in uncertainty due to a longer replenishment leadtime. The system will be modelled using a single-echelon representation and the cost function will be used to derive the parameters (i.e., frequency-of-orders, order level, etc.) that minimize this cost function.