Credit financing in economic ordering policies for defective items with allowable shortages

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 shortages 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. 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] corrected 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 optimal 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 occur. 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 …