Control of Non-instantaneous Degrading Inventory under Trade Credit and Partial Backlogging

  • Pooja Meena Department of Mathematics, University of Rajasthan, Jaipur-302004, India
  • Anil Kumar Sharma Department of Mathematics, Raj Rishi Govt. College, Alwar, India
  • Ganesh Kumar Department of Mathematics, University of Rajasthan, Jaipur-302004, India
Keywords: Inventory control, Weibull deterioration, price-sensitive demand, trade credit, non-instantaneous deterioration

Abstract

Inventory management is an extremely difficult task. It has become usual practice for a provider during the last few decades to provide a retailer with a credit term. In this article, a non-instantly degradable products inventory system is built with a price-sensitive demand and a Weibull credit term allocation reduction rate. Some backlogged deficiencies are permitted. The aim is to maximize the total profit in this study by taking three cases into account. Numerical examples, graphical representations and sensitivity analysis demonstrate the application of the approach developed in this study.

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References

Aggarwal, S. P. and Jaggi, C. K., (2017), “Ordering Policies of Deteriorating Items under Permissible Delay in Payments”, Journal of the Operational Research Society, 46(5):658-662. DOI: https://doi.org/10.1057/jors.1995.90

Ahmad, B. and Benkherouf, L., (2018), “Economic-order-type inventory models for non-instantaneous deteriorating items and backlogging”, RAIRO-Oper. Res., 52(3):895 – 901. DOI: https://doi.org/10.1051/ro/2018010

Akbar, A., Panda, S. G., Sahu, S. and Das, A. K., (2019), “Economic order quantity model for deteriorating item with preservation technology in time dependent demand with partial backlogging and trade credit”, International Journal of Logistics Systems and Management, 32(1) :1.

Amutha, R. and Chandrasekaran, E., (2013), “An inventory model for deteriorating items with three parameters Weibull deterioration and price dependent demand”, J. Eng. Res. Technol., 2 (5) :1931-1935.

Avinadav, T., Herbon, A. and Spiegel, U., (2013), “Optimal inventory policy for a perishable item with demand function sensitive to price and time”, International Journal of Production Economics, 144(2):497-506. DOI: https://doi.org/10.1016/j.ijpe.2013.03.022

Avinadav, T., Herbon, A. and Spiegel, U., (2014), “Optimal ordering and pricing policy for demand functions that are separable into price and inventory age”, International Journal of Production Economics, 155:406-417. DOI: https://doi.org/10.1016/j.ijpe.2013.12.002

Barik,S., Mishra, S., Paikray, S. K. and Misra, U. K., (2013), “An Inventory Model for Weibull Ameliorating, Deteriorating Items under the Influence of Inflation”, International Journal of Engineering Research and Applications, 3:1430 -1436.

Cheng, M. C., Hsieh,T. P., Lee,H. M and Ouyang,L. Y., (2020), “Optimal ordering policies for deteriorating items with a return period and price-dependent demand under two-phase advance sales”, Operational Research, 20:585–604 . DOI: https://doi.org/10.1007/s12351-017-0359-9

Das, D., Roy, A., and Kar, S. (2010). “Improving production policy for a deteriorating item under permissible delay in payments with stock-dependent demand rate”. Computers & Mathematics with Applications, 60(7):1973-1985. DOI: https://doi.org/10.1016/j.camwa.2010.07.031

Das, D., Roy, A., and Kar, S. (2011). “A volume flexible economic production lot-sizing problem with imperfect quality and random machine failure in fuzzy-stochastic environment”. Computers & Mathematics with Applications, 61(9):2388-2400. DOI: https://doi.org/10.1016/j.camwa.2011.02.015

Das, S., Kar, S., and Pal, T. (2014). “Group decision making using interval-valued intuitionistic fuzzy soft matrix and confident weight of experts”. Journal of Artificial Intelligence and Soft Computing Research, 4. DOI: https://doi.org/10.2478/jaiscr-2014-0025

Das, D., Roy, A., and Kar, S. (2015). “A multi-warehouse partial backlogging inventory model for deteriorating items under inflation when a delay in payment is permissible”. Annals of Operations Research, 226(1):133-162. DOI: https://doi.org/10.1007/s10479-014-1691-6

Fenga, L., Chan,Y. L. and Cárdenas-Barrón, L. E., (2017), “Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date”, International Journal of Production Economics, 185:11-20. DOI: https://doi.org/10.1016/j.ijpe.2016.12.017

Ghare, P. M., and Schrader, G. F., (1963), “A model for exponentially decaying inventories”, Journal of Industrial Engineering, 14(5):238-243.

Geetha, K. V. and Udayakumar, R., (2016), “Optimal Lot Sizing Policy for Non-instantaneous Deteriorating Items with Price and Advertisement Dependent Demand Under Partial Backlogging”, International Journal of Applied and Computational Mathematics, 2(2):171–193. DOI: https://doi.org/10.1007/s40819-015-0053-7

Ghosh, P. K., Manna, A. K., Dey, J. K., and Kar, S. (2021). “An EOQ model with backordering for perishable items under multiple advanced and delayed payments policies”. Journal of Management Analytics, 1-32.

Ghosh, S.K. and Chaudhury,K.S., (2004), “An order-level inventory model for deteriorating items with Weibull distribution deterioration, time-quadratic demand, and shortages”, Int. J. Adv. Model. Optim., 6 (1): 31-45.

Giri,B.C., Jalan, A.K. and Chaudhuri, K.S., (2003), “Economic order quantity model with Weibull deteriorating distribution, shortage, and ram-type demand”, Int. J. Syst. Sci., 34: 237-243. DOI: https://doi.org/10.1080/0020772131000158500

Goyal,S. K., (2017), “Economic Order Quantity under Conditions of Permissible Delay in Payments”, Journal of the Operational Research Society, 36(4):335-338. DOI: https://doi.org/10.1057/jors.1985.56

Goyal,S. K. and Chang,C.T., (2009), “Optimal ordering and transfer policy for an inventory with stock dependent demand”, European Journal of Operational Research, 196(1):1177–186. DOI: https://doi.org/10.1016/j.ejor.2008.02.029

Guchhait, P., Maiti, M. K. and Maiti, M., (2013), “Production inventory models for a damageable item with variable demands and inventory costs is an imperfect production process”, International Journal of Production Economics, 144(1):180–188. DOI: https://doi.org/10.1016/j.ijpe.2013.02.002

Gupta,M., Tiwari,S. and Jaggi,C. K., (2018), “Impact of trade credit on inventory models for Weibull distribution deteriorating items with partial backlogging in two-warehouse environment”, International Journal of Logistics Systems and Management, 30(4)(2018), 503.

Halim, M. A., Paul, A., Mahmoud, M., Alshahrani, B., Alazzawi, A. Y. M. and Ismaile, G. M., (2021), “An overtime production inventory model for deteriorating items with nonlinear price and stock dependent demand”, Alexandria Engineering Journal, 60(3): 2779-2786.

Jain, S. and Kumar, M.,(2010), “An EOQ inventory model for items with ramp type demand, three parameters Weibull distribution deterioration and starting with shortages”, Yugoslav Journal of Operational Research, 20(2):249–259. DOI: https://doi.org/10.2298/YJOR1002249J

Jamal, A. M. M., Sarker, B. R and Wang, S., (2017), “An ordering policy for deteriorating items with allowable shortage and permissible delay in payment”, Journal of the Operational Research Society, 48(8):826-833. DOI: https://doi.org/10.1038/sj.jors.2600428

Kawale, S. and Bansode,P., (2012), “An EPQ model using Weibull deterioration for deterioration item with time-varying holding cost”, Int. J. Sci. Eng. Technol. Res., 1 (4): 29-33.

Mahata, P., Mahata, G. C. and De, S. K.,(2018), “ An economic order quantity model under two-level partial trade credit for time varying deteriorating items”, International Journal of Systems Science: Operations & Logistics , 7(1) :1-17. DOI: https://doi.org/10.1080/23302674.2018.1473526

Mishra, U., (2016), “An EOQ with time-dependent Weibull deterioration, quadratic demand and partial backlogging”, International Journal of Applied and Computational Mathematics, 2(4): 545–563. DOI: https://doi.org/10.1007/s40819-015-0077-z

Muriana, C., (2020), “Inventory management policy for perishable products with Weibull deterioration and constrained recovery assumption based on the residual life”, International Journal of Operational Research, 39(4):516 – 538.

Ouyang, L. Y., Wu, K. S. and Yang, C. T., (2006), “A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments”, Computers and Industrial Engineering, 51(4):637–651. DOI: https://doi.org/10.1016/j.cie.2006.07.012

Rastogi, M. and Singh, S. R., (2019), “An inventory system for varying deteriorating pharmaceutical items with price-sensitive demand and variable holding cost under partial backlogging in healthcare industries”, Sadhana, 44(4): 95.

Roy,T. and Chaudhuri, K. S., (2009), “A production-inventory model under stock-dependent demand, Weibull distribution deterioration, and shortage”, Int. Trans. Oper. Res., 16 (3): 325-346 DOI: https://doi.org/10.1111/j.1475-3995.2008.00676.x

Sana, S. S., (2008), “An EOQ model with a varying demand followed by advertising expenditure and selling price under permissible delay in payments: For a retailer”, International Journal of Modelling Identification and Control, 5(2):166-172. DOI: https://doi.org/10.1504/IJMIC.2008.022022

San-Jose, L. A., Sicilia, J. and Alcaide-López-de-Pablo, D., (2018), “An inventory system with demand dependent on both time and price assuming backlogged shortages”, European Journal of Operational Research, 270(3): 889–897. DOI: https://doi.org/10.1016/j.ejor.2017.10.042

San-José, L. A., Sicilia, J., González-De-la-Rosa, M. and Febles-Acosta, J., (2020), “Best pricing and optimal policy for an inventory system under time-and-price-dependent demand and backordering”, Annals of Operations Research, 286:351–369.

Sarkar, B., (2012), “An EOQ model with delay in payments and time varying deterioration rate”, Mathematical and Computer Modelling, 55(3–4):367-377. DOI: https://doi.org/10.1016/j.mcm.2011.08.009

Sarkar, B. and Sarkar S., (2013), “An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand”, Economic Modelling, 30 :924-932 DOI: https://doi.org/10.1016/j.econmod.2012.09.049

Shah,N. H., Chaudhari, U. and Jani, M. Y., (2017), “Optimal Policies for Time-Varying Deteriorating Item with Preservation Technology Under Selling Price and Trade Credit Dependent Quadratic Demand in a Supply Chain”, International Journal of Applied and Computational Mathematics, 3 :363–379. DOI: https://doi.org/10.1007/s40819-016-0141-3

Shah, N. H., Patel, D. G. and Shah, D. B., (2015), “Optimal Pricing and Ordering Policies for Inventory System with Two-Level Trade Credits Under Price-Sensitive Trended Demand”, Int. J. Appl. Comput. Math,1:1101–110 DOI: https://doi.org/10.1007/s40819-014-0003-9

Shaikh, A. A. and Cárdenas-Barrón, L. E., (2020), “An EOQ inventory model for non-instantaneous deteriorating products with advertisement and price sensitive demand under order quantity dependent trade credit”, Revista Investigacion Operacional , 41 (2): 168-187,

Singh,T., Muduly, M. M., Asmita, N., Mallick, C. and. Pattanayak, H., (2020), “A note on an economic order quantity model with time-dependent demand, three-parameter Weibull distribution deterioration and permissible delay in payment”, Journal of Statistics and Management Systems, 23(3): 643-662

Soni, H. N., (2013), “Optimal replenishment policies for non-instantaneous deteriorating items with price sensitive demand under permissible delay in payments”, International Journal of Production Economics, 146(1):259–268. DOI: https://doi.org/10.1016/j.ijpe.2013.07.006

Sundararajan, R., Vaithyasubramanian S., and Nagarajan, A., (2020), “Impact of delay in payment, shortage and inflation on an EOQ model with bivariate demand”, Journal of Management Analytics, 8(2):267-294.

Tripathi, R. P. and Chaudhary, S. K, (2017), “Inflationary induced EOQ model for Weibull distribution deterioration and trade credits”, International Journal Applied and Computational Mathematics, 3(4):3341–3353. DOI: https://doi.org/10.1007/s40819-016-0298-9

Tripathi, R.P. and Pandey, H. S., (2020), “ Optimal ordering policies for non-instantaneous Weibull deteriorating items with price linked demand under trade credits”, International Journal of Supply Chain and Inventory Management, 3(2) :77 – 92.

Tripathi, R. P., Singh, D. and Aneja, S., (2018), “Inventory models for stock-dependent demand and time-varying holding cost under different trade credits”, Yugoslav Journal of Operations Research, 28(1):139–151. DOI: https://doi.org/10.2298/YJOR160317018T

Udayakumar, R., Geetha, K. V., and Sana, S. S., (2020), “Economic ordering policy for non-instantaneous deteriorating items with price and advertisement dependent demand and permissible delay in payment under inflation”, Mathematical Methods in the Applied Sciences, 44(9) :1-25

Wu, K. S., Ouyang, L. Y. and Yang, C. T., (2009), “Coordinating replenishment and pricing policies for non-instantaneous deteriorating items with price-sensitive demand”, International Journal of Systems Science, 40(12):1273–1281. DOI: https://doi.org/10.1080/00207720903038093

Published
2021-12-11
How to Cite
Meena, P., Sharma, A. K., & Kumar, G. (2021). Control of Non-instantaneous Degrading Inventory under Trade Credit and Partial Backlogging. Operational Research in Engineering Sciences: Theory and Applications, 4(3), 122-141. https://doi.org/10.31181/oresta111221122m