Simultaneous Optimization of Contingent and Advance Purchase Orders with Fixed Ordering Costs

We analyze a finite horizon periodic-review inventory model in the presence of advance purchase discount (APD). In addition to the opportunity to place a contingent order when required, the buyer can also commit to advance orders and receive discounts. Thus the buyer faces the following tradeoff: Contingent orders provide operational flexibility to respond to uncertain demands at a high purchase cost, whereas advance orders incur low purchase cost while sacrificing operational flexibility. We consider a simple and easy-to-implement APD scheme in which the buyer enjoys price discounts by committing at the outset to a fixed size of advanced order for each period along with contingent orders when required. We first show that for any given advance order size, an advance-order dependent (s, S) policy is optimal. We then find the advance order size together with the corresponding (s, S) policy that minimizes the buyer’s total cost.