The algorithm for the optimal cycle time and pricing decisions for an integrated inventory system with order-size dependent trade credit in supply chain management

A given inventory problem consists of two parts: (1) the modeling part and (2) the solution procedure part. The modeling part can provide insight into the solution of the inventory problem and the solution procedure part involves the implementation of the inventory model. Both the modeling part and the solution procedure part of the inventory problem are equally important. Recently, Ouyang et al. [17] developed an integrated inventory model with a price-sensitive demand rate and determined both the economic lot size of the buyer's ordering and the supplier's production batch in order to maximize the total profit per unit time Basically, their modeling is correct and interesting. They developed an algorithm based upon the firstorder condition and the second-order condition to locate the optimal solution. However, the fundamentals of mathematics and the numerical examples which are considered in this paper illustrate that their algorithm based upon the first-order condition and the second-order condition to locate the optimal solution has several shortcomings. These shortcomings are shown here to influence the accuracy of the implementation of the inventory model. Since there exist reasons and motivations to present the correct solution procedures to the targeted readers, the main purpose of this paper is to adopt the rigorous methods of mathematical analysis in order to develop the complete solution procedures to locate the optimal solution for removing shortcomings in the earlier investigation by Ouyang et al. [17]. (C) 2015 Elsevier Inc. All rights reserved.