Effect of Delayed Payments (Trade Credit) on Order Quantities

We address the problem of determining the economic order quantity when the vendor permits delay in payment. Some early researchers argued that the best order quantity is invariant with respect to the trade credit. Others argued that the order quantity should increase as the delay in payment increases. We analyse this problem using the discounted cash-flow approach, and provide clarification on the inconsistencies between these approaches. First, we show that the best order quantity is an increasing function of the permitted delay in payment. We also show that an approach suggested by Chand and Ward not only yields an upper bound on the optimum, but also provides robust results. Though the classical square-root formula disregards trade-credit information, under some circumstances, it will yield better results than the formulation taking into account that information. We illustrate this anomaly with an example, and provide analytical explanation for it. We also discuss some potential conceptual pitfalls in using the average cost analysis as an approximation to the discounted cash-flow approach.