Credit financing in economic ordering policies for defective items with allowable shortages Chandra K. Jaggi a,⇑ , Satish K. Goel a , Mandeep Mittal b a Department of Operational Research, Faculty of Mathematical Sciences, New Academic Block, University of Delhi, Delhi 110007, India b Department of Computer Science Engineering, Amity School of Engineering and Technology, 580 Delhi Palam Vihar Road, Bijwasan, New Delhi 110061, India article info Keywords: Inventory Imperfect items Shortages Permissible delay abstract In the classical inventory models, the common unrealistic assumption is that all the items produced are of good quality in nature. However, in realistic environment, it can be observed that there may be some defective items in an ordered lot. These items are usually picked up during the screening process and are sold as a single lot at the end of screening process. Further, it is tacitly assumed that the supplier must be paid for the items as soon as the items are received. Whereas, in today business transaction, it is common to see that the retailer is allowed some grace period before they settle the account with the supplier. Under this scenario, a new inventory model for imperfect quality items has been developed under permissible delay in payments. Shortages are allowed and fully backlogged, which are eliminated during screening process as it has been assumed that screening rate is greater than the demand rate. This model jointly optimizes the order quantity and short- ages by maximizing the expected total profit. Results have been validated with the help of numerical example using Matlab 7.0.1. Comprehensive sensitivity analysis has also been presented. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction In today’s technology driven world, despite of efficient planning of manufacturing system and emergence of sophisticated production methods and control systems; the items produced may have some fraction of defectives. By considering this fact, researchers devoted a great amount of effort to develop EPQ/EOQ models for defective items [1–5]. In 2000, Salameh and Jaber [6] extended the traditional EPQ/EOQ model for the imperfect quality items. They also considered that the imperfect – quality items are sold at a discounted price as a single batch by the end of the screening process. Cárdenas-Barrón [7] cor- rected the optimum order size formula obtained by Salameh and Jaber [6] by adding constant parameter which was missing in their optimum order size formula. Further, Goyal and Cárdenas-Barrón [8] presented a simple approach for determining economic production quantity for imperfect quality items and compare the results based on the simple approach with opti- mal method suggested by Salameh and Jaber [6], which results in almost zero penalty. Papachristos and Konstantaras [9] examined the Salameh and Jaber [6] paper closely and rectify the proposed conditions to ensure that shortages will not oc- cur. They extended their model to the case in which withdrawing takes place at the end of the planning horizon. Further, Wee et al. [10] extended the model of Salameh and Jaber [6] for the case where shortages are back ordered in each cycle. They also studied the effect of varying backordering cost value and showed that as the backordering cost increases then the rate of change in their annual profit decreases as compared to that in Salameh and Jaber [6] model. Maddah and Jaber 0096-3003/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.amc.2012.11.027 ⇑ Corresponding author. E-mail address: ckjaggi@yahoo.com (C.K. Jaggi). Applied Mathematics and Computation 219 (2013) 5268–5282 Contents lists available at SciVerse ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc