Optimal purchasing cycle length of a deteriorating product for intermediary firms

In a supply chain logistics system, the function of an intermediary firm is to purchase products and to sell those purchased products to the public or to other firms. This article investigates how an intermediary firm can optimally determine the purchasing cycle length of a deteriorating product. By incorporating the special structure of the intermediary firm's environments and the deteriorating nature of the product, the inventory problem encountered by the intermediary firm is mathematically formulated. The optimal purchasing cycle length is derived such that the total profit is maximized. Several interesting properties of the optimal policy are investigated and an efficient iterative algorithm is provided to search for the optimal policy. Also, the convergence of the iterative algorithm developed in this paper is proved. Finally, a numerical example is provided to illustrate the features of the proposed problem and the iterative search algorithm.