Learning effect on an optimal policy for mathematical inventory model for decaying items under preservation technology with the environment of COVID-19 pandemic

Subhash Kumar; Ashok Kumar; Madhu Jain

doi:10.26637/MJM0804/0063

Abstract

Due to the environment of corona virus pandemic, a huge problem arises in the market, due to which the retailer keeps his items lying, and those items start to deteriorate. He is unable to get the new goods from suppliers and get a shortage. We established an optimal policy for mathematical inventory model for decaying items under preservation technology (PT) with learning effect. This model is starting with partially backlogging shortage. The investment in Preservation technology is used so that the items deposited with the retailer do not deteriorate. In this model learning effect and preservation technology plays a very important role. Which the help of the total cost is reduced and maintains the quality of the environment. We show that the total cost is a convex function. Finally, some figures are presented to highlight the numerical examples and sensitivity results. And performed using the Mathematicia-9.0 software.

Keywords:

Covid-19 environment, Decaying items, Learning effect, Preservation technology, Shortage, Ramp type demand

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Subhash Kumar Department of Mathematics, Meerut College, Meerut-250003, Uttar Pradesh, India.
Ashok Kumar Department of Mathematics, Meerut College, Meerut-250003, Uttar Pradesh, India.
Madhu Jain

Pages: 1694-1702
Date Published: 01-10-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

Ghare, P.M, and Schrader, G.H. A model for an exponentially decaying inventory. Journal of Industrial Engineering, 14(5), (1963), 238-243.

Mandal, B.N., and Phaujdar, S. An inventory model for deteriorating items and stock dependent consumption rate. J. Oper. Res. Soc. 40(5), (1989), 483-488.

Fujiwara, O., Perera, U.L.J.S.R. EOQ models for continuously deteriorating products using linear and exponential penalty costs. Eur. J. Oper. Res. 70(1), (1993), 104-114.

Mandal, B., and Pal, A. K. Order level inventory system with ramp type demand rate for deteriorating items. Journal of Interdisciplinary Mathematics, 1(1), (1998), $49-66$.

Chang, H.J., and Dye, C.Y. An EOQ model for deteriorating items with time varying demand and partial back logging. Journal of the Operational Research Society, 50(11), (1999), 1176-1182.

Goyal S, Giri B. . Recent trends in modeling of deteriorating inventory. European Journal of Operational Research, 134(1), (2001), 1-16.

Papachristos P, Skouri K. An inventory model with deteriorating items, quantity discount, pricing and timedependent partial backlogging. International Journal of Production Economics, 83(10),(2003), 247-256.

Wu, K.S, Ouyang L.Y. and Yang, C.T. An optimal replenishment policy for non- instantaneous deteriorating items with stock-dependent demand and partial backlogging. International Journal of Production Economics, 101(2), (2006), 369-384.

Ouyang, L.Y. Wu, K.S. and Yang C.T. A study on an inventory model for non- instantaneous deteriorating items with permissible delay in payments. Computers & Industrial Engineering, 51(4), (2006), 637-651.

Panda, S., Senapati, S., and Basu, M. Optimal replenishment policy for perishable seasonal products in a season with ramp-type time dependent demand. Computers and Industrial Engineering, 54 (2), (2008), 301-314.

Skouri, K., Konstantaras, I., Papachristos, S., and Ganas, I. Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate. European Journal of Operational Research, 192(1), (2009), 79-92. doi:10.1016/j.ejor.2007.09.003

Skouri, K., Konstantaras, I., Papachristos, S., and Ganas, I. Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate. European Journal of Operational Research, 192(1), (2010), 79-92.

Hsu, P.H., Wee, H.M., and Teng, H.M. Preservation technology investment for deteriorating inventory, International Journal of Production Economics, 124(2), (2010), 388-394.

Bakker, M., Riezebos, J. and Teunter, R.H. Review of inventory systems with deterioration since 2001. European Journal of Operational Research, 221(2), (2012), $275-284$.

Dye, C.Y. and Hsieh, T.P. An optimal replenishment policy for deteriorating items with effective investment in preservation technology. European Journal of Operational Research, 218(2012), 106-112.

Glock, C.H., Schwindl, K. and Jaber, M.Y. An EOQ model with fuzzy demand and learning in fuzziness, $I n-$ ternational Journal of Services and Operations Management, 12(1), (2012), 90-100.

Cai, X., Chen J., Xiao Y., and Gang Y. Fresh-product supply chain management with logistics outsourcing. Omega, 41(4), (2013), 752-765.

Kumar, N., Singh, S.R. and Kumari, R. Learning effect on an inventory model with two-level storage and partial backlogging under inflation, International Journal of Services and Operations Management, 16(1), (2013), $98-118$.

Hsieh, T.P. and Dye, C.Y. A production inventory model incorporating the effect of preservation technology investment when demand is fluctuating with time. Journal of Computational and Applied Mathematics, 239(2013), 25-36.

Dye, C.-Y. The effect of preservation technology investment on a non-instantaneous deteriorating inventory model. Omega, 41(5), (2013), 872-880.

Pal, S., Mahapatra, G.S. and Samanta, G.P. A production inventory model for deteriorating item with ramp type demand allowing inflation and shortages under fuzziness. Economic Modelling, 46(2015), 334-345.

Sicilia, J., González-De-la-Rosa, M., Febles-Acosta, J., & Alcaide-López-de-Pablo, D. An inventory model for deteriorating items with shortages and time-varying demand. International Journal of Production Economics, 155(2014), 155-162.

Muriana, C., Effectiveness of the food recovery at the retailing stage under shelf life uncertainty: an application to Italian food chains. Waste Manag, 41(2015), 159-168.

Prasad,K., and Mukherjee, B. Optimal inventory model under stock and time dependent demand for time varying deterioration rate with shortages, Annals of Operations Research, (2016), 1572-9338.

Zhang, J., Wei, Q., Zhang, Q., and Tang, W. Pricing, service and preservation technology investments policy for deteriorating items under common resource constraints. Computers & Industrial Engineering, 95(2016), 1-9.

Luo, X.-R. Analysis of inventory models with ramp type demand, Journal of Interdisciplinary Mathematics, 20(2), (2017), 543-554.

Singh, T., Sethy, N. N., and Nayak, A.K. An Ordering Policy with generalized deterioration, ramp-type demand under complete backlogging. Logistics, Supply Chain and Finanicial Predictive Analytics, (2018), 43-55.

Huang, H., He, Y., and Li, D. Pricing and inventory decisions in the food supply chain with production disruption and controllable deterioration. Journal of Cleaner Production, 180(2018), 280-296.

Suthar, M. S., and Shukla K. T. Pricing and ordering policy for deteriorating inventory system with price sensitive ramp type demand, pre and post deterioration discounts. Revista investigation operational, 40(2), (2019), 267-274.

Liu,L., Zhao,L. and Ren,X. Optimal preservation technology investment and pricing policy for fresh Food. Computers & Industrial Engineering, 135(2019), 746-756.