Ann Oper Res DOI 10.1007/s10479-014-1739-7 An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation- and selling price-dependent demand and customer returns Maryam Ghoreishi · Gerhard-Wilhelm Weber · Abolfazl Mirzazadeh © Springer Science+Business Media New York 2014 Abstract This paper develops an economic ordering policy model for non-instantaneous deteriorating items with selling price- and inflation-induced demand under the effect of inflation, permissible delay in payments and customer returns. Shortages are allowed and partially backlogged. The customer returns are assumed to increase with both the quantity sold and the product price. The main objective is to determine the optimal selling price, the optimal length of time in which there is no inventory shortage, and the optimal replenishment cycle simultaneously, to minimize the present value of the total profit. An efficient algorithm is presented to find the optimal solution of the developed model. Finally, a numerical example is extracted to solve the presented inventory model using the proposed algorithm. Keywords Optimal pricing and inventory · Permissible delay in payments · Non-instantaneous deteriorating items · Customer returns · Inflation 1 Introduction Recently, many researchers have studied the inventory problems for deteriorating items such as fashionable items, electronics products, fruits, and green vegetables, and many others. Ghare and Schrader (1963) was the first to establish an economic order quantity (EOQ) model for deteriorating items. Afterward, Covert and Philip (1973) extended their work by presenting a variable rate of deterioration. Goyal and Giri (2001) presented a great literature M. Ghoreishi (B ) · A. Mirzazadeh Department of Industrial Engineering, Kharazmi University, Shahid Mofatteh Street, 15719-14911 Tehran, Iran e-mail: m_ghoreishi14@yahoo.com A. Mirzazadeh e-mail: a.mirzazadeh@aut.ac.ir G.-W. Weber Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey e-mail: gweber@metu.edu.tr 123