Abstract
In the production process, the issue of quality is always ignored which results in defective production. These defective items can be removed from the lot through the inspection process which becomes essential for the system. Demand is considered as stock dependent. It is continuously declined to meet the customer’s demand which depends on the on-hand inventory up to the time t2. After that the inventory level declines by constant demand up to time t3. Thereafter, shortages occur and it accumulates at the rate \( \psi \left( {\tau - t} \right)\,till\,t = \tau \) when the next batch arrives. The whole cycle repeats itself after the cycle length τ. Further, it is assumed that payment will be made to the supplier for the goods immediately after receiving the consignment. Whereas, in practice, supplier does offer a certain fixed period to the retailer for settling the account. During this period, supplier charges no interest, but beyond this period interest is being charged. On the other hand, retailer can earn interest on the revenue generated during this period. Keeping this scenario in mind, an attempt has been made to formulate an inventory policy for the retailer dealing with imperfect quality items under permissible delay in payments. Results have been analyzed with the help of a numerical example and sensitivity analysis also carried out.
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References
Baker RC, Urban TL (1988) A deterministic inventory system with an inventory level dependent demand rate. J Oper Res Soc 39:823–831
Baron et al (2018) Retailer’s joint ordering, pricing, and preservation technology investment policies for a deteriorating item under permissible delay in payments. Math Prob Eng 1–14
Bhunia AK, Shaikh AA (2011) A deterministic model for deteriorating items with displayed inventory level dependent demand rate incorporating marketing decision with transportation cost. Int J Ind Eng Comput 2(3):547–562
Bhunia AK, Shaikh AA (2014) A deterministic inventory model for deteriorating items with selling price dependent demand and three-parameter Weibull distributed deterioration. Int J Ind Eng Comput 5(3):497–510
Bhunia AK, Shaikh AA, Maiti AK, Maiti M (2013) A two warehouse deterministic inventory model for deteriorating items with a linear trend in time dependent demand over finite time horizon by Elitist Real-Coded Genetic Algorithm. Int J Ind Eng Comput 4(2):241–258
Bhunia AK, Shaikh AA, Pareek S, Dhaka V (2015) A memo on stock model with partial backlogging under delay in payments. Uncertain Supply Chain Manag 3:11–20
Chand S, Ward J (1987) A note on economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 38:83–84
Chang CT (2004) Inventory models with stock dependent demand and nonlinear holding costs for deteriorating items. Asia Pac J Oper Res 21:435–446
Datta TK, Pal AK (1990) A note on an inventory-level-dependent demand rate. J Oper Res Soc 41:971–975
Datta TK, Paul K (2001) An inventory system with stock-dependent, price-sensitive demand rate. Prod Plan Control 12:13–20
Goyal SK, Chang CT (2009) Optimal ordering and transfer policy for an inventory with stock dependent demand. Eur J Oper Res 196:177–185
Goyal SK (1985) Economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 36(4):335–338
Hou KL, Lin LC (2006) An EOQ models for deteriorating items with price & stock- dependent selling rate under inflation & time value of money. Int J Syst Sci 37:1131–1139
Jaggi CK, Cardenas-Barron LE, Tiwari S, Shafi AA (2017) Two warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments Sharif University of Technology. Sci Iran E 24(1):390–412
Jaggi CK, Goel SK, Mittal M (2013) Credit financing in economic ordering policies for defective items with allowable shortages. Appl Math Comput 219:5268–5282
Levin RI, McLaughlin CP, Lamone RP, Kottas JF (1972) Production/operations management: contemporary policy for managing operating systems. McGraw-Hill, New York
Mandal BN, Phaujdar S (1989) An inventory model for deteriorating items and stock-dependent consumption rate. J Oper Res Soc 40:483–488
Padmanabhan G, Vrat P (1995) EOQ models for perishable items under stock-dependent selling rate. Eur J Oper Res 86:281–292
Pal P, Das CB, Panda A, Bhunia AK (2005) An application of real-coded genetic algorithm (for mixed integer non-linear programming in an optimal two-warehouse inventory policy for deteriorating items with a linear trend in demand and a fixed planning horizon. Int J Comput Math 82:163–175
Pal S, Goswami A, Chaudhari KS (1993) A deterministic inventory model for deteriorating items with stock dependent rate. Int J Prod Econ 32:291–299
Salameh MK, Jaber MY (2000) Economic production quantity model for items with imperfect quality. Int J Prod Econ 64:59–64
Sarkar et al (2018) A model for imperfect production system with probabilistic rate of imperfect production for deteriorating products. DJ J Eng Appl Math 4(2):1–12
Silver EA, Peterson R (1985) Decision systems for inventory management and production planning, 2nd edn. Wiley, Newyork
Tsu-Pang H, Chang-Yuan D, Liang-Yuh O (2010) Optimal lot size for an item with partial backlogging rate when demand is stimulated by inventory above a certain stock level. Math Comput Model 51:13–32
Urban TL (1992) An inventory model with an inventory level dependent demand rate & relaxed terminal condition. J Oper Res Soc 43:721–724
Whitin TM (1957) The theory of inventory management. Princeton University Press, Princeton
Wolfe HB (1968) A model for control of style merchandise. Ind Manag Rev 9:69–82
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Dhaka, V., Pareek, S., Mittal, M. (2020). Stock-Dependent Inventory Model for Imperfect Items Under Permissible Delay in Payments. In: Shah, N., Mittal, M. (eds) Optimization and Inventory Management. Asset Analytics. Springer, Singapore. https://doi.org/10.1007/978-981-13-9698-4_10
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