An economic order quantity model with partial backordering and incremental discount Ata Allah Taleizadeh a , Irena Stojkovska b , David W. Pentico c,⇑ a School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran b Department of Mathematics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, Skopje, Macedonia c Palumbo-Donahue School of Business, Duquesne University, Pittsburgh, PA 15282, USA article info Article history: Received 14 August 2014 Received in revised form 2 December 2014 Accepted 5 January 2015 Available online 14 January 2015 Keywords: EOQ Incremental discounts Full backordering Partial backordering abstract Determining an order quantity when quantity discounts are available is a major interest of material managers. A supplier offering quantity discounts is a common strategy to entice the buyers to purchase more. In this paper, EOQ models with incremental discounts and either full or partial backordering are developed for the first time. Numerical examples illustrate the proposed models and solution methods. Ó 2015 Elsevier Ltd. All rights reserved. 1. Introduction and literature review Since Harris (1913) first published the basic EOQ model, many variations and extensions have been developed. In this paper we combine two of those extensions: partial backordering and incremental quantity discounts. Montgomery, Bazaraa, and Keswani (1973) were the first to develop a model and solution procedure for the basic EOQ with partial backordering (EOQ–PBO) at a constant rate. Others taking somewhat different approaches have appeared since then, including Pentico and Drake (2009), which will be one of the two bases for our work here. In addition, many authors have developed models for the basis EOQ-PBO combined with other situational characteristics, such as Wee (1993) and Abad (2000), both of which included a finite production rate and product deterioration, Sharma and Sadiwala (1997), which included a finite production rate with yield losses and transportation and inspection costs, San José, Sicilia, and García-Laguna (2005), which included models with a non-constant backordering rate, and Taleizadeh, Wee, and Sadjadi (2010), which included production and repair of a number of items on a single machine. Descriptions of all of these models and others may be found in Pentico and Drake (2011). Enticing buyers to purchase more by offering either all-units or incremental quantity discounts is a common strategy. With the all-units discount, purchasing a larger quantity results in a lower unit purchasing price for the entire lot, while incremental dis- counts only apply the lower unit price to units purchased above a specific quantity. So the all-units discount results in the same unit price for every item in the given lot, while the incremental dis- count can result in multiple unit prices for an item within the same lot (Tersine, 1994). In the following we focus on the research using only an incremental discount or both incremental and all-units dis- counts together. Since Benton and Park (1996) prepared an exten- sive survey of the quantity discount literature until 1993, we will describe newer research, along with a short history of incremental discounts and older research which is more related to this paper. The EOQ model with incremental discounts was first discussed by Hadley and Whitin (1963). Tersine and Toelle (1985) presented an algorithm and a numerical example for the incremental dis- count and examined the methods for determining an optimal order quantity under several types of discount schedules. Güder, Zydiak, and Chaudhry (1994) proposed a heuristic algorithm to determine the order quantities for a multi-product problem with resource limitations, given incremental discounts. Weng (1995) developed different models to determine both all-units and incremental dis- count policies and investigated the effects of those policies with increasing demand. Chung, Hum, and Kirca (1996) proposed two coordinated replenishment dynamic lot-sizing problems with both incremental and all-units discounts strategies. Lin and Kroll (1997) extended a newsboy problem with both all-units and incremental discounts to maximize the expected profit subject to a constraint that the probability of achieving a target profit level is no less than http://dx.doi.org/10.1016/j.cie.2015.01.005 0360-8352/Ó 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: taleizadeh@ut.ac.ir (A.A. Taleizadeh), irenatra@pmf.ukim.mk, irena.stojkovska@gmail.com (I. Stojkovska), pentico@duq.edu (D.W. Pentico). Computers & Industrial Engineering 82 (2015) 21–32 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie