A note on optimal ordering policies of EOQ model under discount of purchase price or increase of setup cost

The traditional EOQ model assumes that both the setup cost and the purchase cost are independent of the lot size. Matsuyama (2001) modifies the traditional EOQ model such that the setup cost increases as the ordering quantity increases or the purchase cost decreases as the ordering quantity increases. Both Theorem 3 and Corollary 3 in Matsuyama (2001) explore the optimal solution of the average profit per one ordering quantity when the purchase price discount which depends on the ordering quantity. Moreover, both Theorem 5 and Corollary 5 in Matsuyama (2001) determine the optimal solution of the average profit per one ordering quantity when the setup cost which depends on the ordering quantity. Basically, the arguments of Theorem 3, Corollary 3, Theorem 5 and Corollary 5 in Matsuyama (2001) are not complete. Some situations do not be discussed in Matsuyama (2001). Therefore, the main purpose of this paper is to complement the shortcomings of Matsuyama (2001) and to present another alternatives to give complete proofs to Matsuyama (2001). Furthermore, this paper reveals simple solution procedures to find the optimal solutions of the inventory models described in Matsuyama (2001). Finally, numerical examples are used to explain all results obtained by this paper.