A comprehensive extension of the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity

Recently, Kreng and Tan [Expert Systems with Applications 37 (2010) 5514–5522] developed an economic order quantity (EOQ) model under two levels of trade credit policy in which the supplier offers to the wholesaler a permissible delay period M, and the wholesaler also provides its retailers a permissible delay period N (with M > N). In this paper, we point out some inappropriate mathematical expressions in both interest charged and interest earned in Kreng and Tan. For generality, we then extend their model to allow the following facts: (1) the interest rate Ic charged by the supplier is not necessarily higher than the interest rate Ie earned by the wholesaler, and (2) the permissible delay period M offered by the supplier is independent of the permissible delay period N offered by the wholesaler. Furthermore, we study the necessary and sufficient conditions for finding the optimal solution, and thus establish several theoretical results to characterize the solution that provides the minimum annual total relevant cost. Finally, numerical examples are given to illustrate the theoretical results and obtain some managerial insights.