Retailer’s Economic Ordering Quantity under Partial Payments Delay: an Algebraic Approach

The main purpose of this paper is to investigate the optimal retailer’s lot-sizing decisions under partial payments delay within the economic order quantity (EOQ) framework. All previously published models concerned with payments delay assumed that the supplier would offer the retailer fully payments delay. However, in this paper, we assume that the supplier would offer the retailer partial payments delay. That is, the retailer must make a partial payment to the supplier when the order is received. Then the retailer must pay off the remaining balance at the end of the permissible delay period. Furthermore, we adopt the assumption that the retailer’s unit selling price and the purchasing price per unit are not necessarily equal. Under these conditions, we model the retailer’s inventory system and an algebraic approach is provided to find the optimal solution. One theorem is developed to efficiently determine the optimal lot-sizing decisions for the retailer. Finally, numerical examples are given to illustrate the theoretical results and to draw managerial insights.