An EOQ model with allowable shortage under trade credit in different scenario Chandra K. Jaggi a,⇑ , V.S.S. Yadavalli b , Mona Verma c , Anuj Sharma a a Department of Operational Research, Faculty of Mathematical Sciences, New Academic Block, University of Delhi, Delhi 110007, India b Department of Industrial & Systems Engineering, Building: Engineering II, Room 3-10, University of Pretoria, 0002 Pretoria, South Africa c Department of Management Studies, Shaheed Sukhdev College of Business Studies (University of Delhi), Vivek Vihar, Delhi 110095, India article info Keywords: Inventory EOQ Trade credit Fully backlogged shortage abstract In present business culture, usually supplier offers a permissible delay in payments to retailer in order to stimulate his demand. However, while developing the inventory model with shortages under permissible delay in payments, it has been observed, in the literature, that researcher have not considered the fact that retailer can earn interest on the revenue generated after fulfilling the outstanding demand as soon as his new consignment arrives at the beginning of the cycle. Thus, the revenue along with the interest earn can be utilized to pay off the amount at the of credit period. At this point of time there may be two sce- narios, either he has enough amounts to settle the account with the supplier or delay incur- ring interest charges on the unpaid/overdue balance and the determination of a retailer’s pay off time, after the expiring of credit period, is largely affected by his interest income and interest payable. Owing to these facts, a retailer cost minimization inventory model has been developed for each scenario which jointly optimizes the cycle length and stock-in period. The model has been validated with the help of numerical example. Sensi- tivity analysis along with its economic interpretation has been also presented. Ó 2014 Elsevier Inc. All rights reserved. 1. Introduction In recent business environment trade credit is used as a tool by a supplier to encourage the retailer to procure a greater volume of goods, to earn a reasonable profit. On the other hand, trade credit offers a lower unit purchasing cost as well as representing an important source of short-term external finance for retailers. During this period no interest is being charged by the supplier, but beyond this period an interest is charged by the supplier under the terms and conditions agreed upon. Teng [14] illustrated two more benefits of trade credit period, firstly it attracts new buyers who consider it to be a type of price reduction, and secondly it may be applied as an alternative to price discount because it does not provoke competitors to reduce their prices and thereby introduces lasting price reductions. Moreover, the policy of granting credit terms adds not only an additional cost but also an additional dimension of default risk to the supplier (Teng et al. [15]). In the literature, the extensive use of trade credit as an alternative has been addressed by Goyal [6] who first developed an economic order quantity model under the conditions of permissible delay in payments in which he calculated interest based on the purchasing cost of goods sold within the permissible delay period. Further, Aggarwal and Jaggi [1] developed the inventory model with an exponential deterioration rate under the condition of permissible delay in payments. Jamal et al. [10] further generalized the model with shortages. Chung [3] developed an alternative approach to the Goyal’s [6] problem. http://dx.doi.org/10.1016/j.amc.2014.12.040 0096-3003/Ó 2014 Elsevier Inc. All rights reserved. ⇑ Corresponding author. E-mail addresses: ckjaggi@or.du.ac.in, ckjaggi@yahoo.com (C.K. Jaggi). Applied Mathematics and Computation 252 (2015) 541–551 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc