two-warehouse inventory model having a percentage defective items is formulated and solved by introducing proportionate discount for imperfect quality items, where the warehouses possessa fixed capacity in contrast with the traditional inventory model which is assumed to have unlimited capacity. For the present model it is assumed that the inventory costs in rented warehouse(RW) is higher than the own warehouse(OW). The aim of this paper is to find the optimal lot size to maximize the total profit for the developed model by introducing the proportionate rate of discount for items with imperfect quality.Numerical example is provided to illustrate the results of the proposed model.The concavity of the profit function is shown graphically. Sensitivity analysis is conducted toshow the applicability of the proposed model by changing the values of different parameters presentin the derived mathematical expressions for both the actual lot size and the profit.
warehouse, proportionate discount, inventory
. V.R. Hartely, Operations Research: A Managerial Emphasis,’ Santa Monica, CA: Good Year, 1979, pp. 315–317.
. K.V.S. Sarma, A deterministic order-level inventory model for deteriorating items with twostorage facilities, 1987, European Journal of Operational Research, vol. 29, pp.70–72.
. A. GoswamiandK. S. Chaudhuri, An Economic order quantity model for items with two levels of storage for a linear trend in demand, 1992, Journal of Operational Research Society, vol. 43, pp. 157–167.
. A.K. Bhuniaand M. Maiti, A two-warehouse inventory model with linear trend in demand, 1994, Opsearch, vol. 31, pp. 318–329.
. I. Benkherouf, A deterministic order level inventory model for deteriorating items with twostorage facilities, 1997, International Journal of Production Economics, vol. 48, pp. 167–175.
. A.K. Bhuniaand, M. Maiti, A two-warehouse inventory model for deteriorating items with a linear trend in demand and shortages, 1998, Journal of Operational Research Society, vol. 49, pp. 287–292.
. Y.W. Zhou, An optimal eoq model for deteriorating items with two warehouses and time varying demand, 1998, Mathematica Applicata, vol. 10, pp. 19–23.
. M.K. Salameh, M.Y. Jaber, Economic production quantity model for items with imperfect quality, 2000, International journal of Production Economics, vol. 64, pp. 59-64.
. S. Kar, A.K. Bhuniaand, M. Maiti, Deterministic inventory model with two levels of storage, a linear trend in demand and a fixed time horizon, 2001, Computers and Operations Research, vol. 28, pp. 1315–1331.
. H.L. Yang, Two-warehouse inventory models for deteriorating items with shortages under inflation, 2004, European Journal of Operational Research, vol. 157, pp. 344–356.
. Y.W. Zhou, S.L. Yang, A two-warehouse inventory model for items with stock-level-dependent demand rate, 2005, International Journal of Production Economics, vol. 95, pp. 215–228.
. C.C. Lee, Two-warehouse inventory model with deterioration under FIFO dispatching policy, 2006, European Journal of Operational Research, vol. 174, pp. 861–873.
. H.L. Yang, Two-warehouse partial backlogging inventory models for deteriorating items under inflation, 2006, International Journal of Production Economics, vol. 103, pp. 362–370.
. K.J. Chung, T.S. Huang, The optimal retailer’s ordering policies for deteriorating items with limited storage capacity under trade credit financing, 2007, International Journal of Production Economics, vol. 106, pp. 127–145.
. B. Das, K. Maity, M. Maiti, A two warehouse supply chain model under possibility/necessity/credibility measures, 2007, Mathematical and Computer Modelling, vol. 46, pp. 398–409.
. C.Y. Dye, L.Y. Ouyang, T.P. Hsieh, Deterministic inventory model for deteriorating itemswith capacity constraint and time-proportional backlogging rate, 2007, European Journal of Operational Research, vol. 178, pp. 789–807.
. B. Niu, J. Xie, A note on Two-warehouse Inventory Model with Deterioration under FIFO dispatch policy, 2008, European Journal of Operational Research, vol. 190, pp. 571–577.
. M. Rong, N.K. Mahapatraand, M. Maiti, A two warehouse inventory model for a deteriorating item with partially/fully backlogged shortage and fuzzy lead time, 2008, European Journal of Operational Research, vol. 189, pp. 59–75.
. K.J. Chung, C.C. Her, S.D. Lin, A two-warehouse inventory model with imperfect quality production processes, 2009, Computers & Industrial Engineering, vol. 56, pp. 193–197.
. T.Y. Lin., Y.H. Chin, A two-warehouse inventory model foritems with imperfect quality and penaltycosts under screening errors, 2013, Journal of Information and Optimization Sciences, pp. 433–450.
. C.K. Jaggi, S. Tiwari, A.A. Shafi, Effect of deterioration on two-warehouse inventory model with imperfect quality, 2015, Computers & Industrial Engineering, vol. 88, pp. 378–385.
. P. Saxena, S.R. Singh, I. Sangal, A two warehouse production inventory model with trade credit under reliability consideration, 2016, Uncertain Supply Chain Management, vol. 4, pp. 319–330.
. C.K. Jaggi, L.E. Cardenas-Barron, S. Tiwariand, A.A. Sha, Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments, 2017, Scientia Iranica E, vol. 24, no. 1, pp. 390-412.
. N.K.Kaliraman, R. RAJ, S.Chandra, H. Chaudhary, Two warehouse inventory model for deteriorating item with exponential demand rate and permissible delay in payment, 2017, Yugoslav Journal of Operations Research, vol. 27, no. 1, pp. 109-124.