An Inventory Model for Perishable Goods with Controllable Deterioration, Partially Backlogged Shortage and Advanced Payment

Anima Bag¹ , Rojalini Patro²

1. Department of Statistics, Faculty, Rama Devi Women’s University, Bhubaneswar, India.
2. Department of Mathematics, Faculty, K L Deemed to be University, Vijayawada, India.

Section:Research Paper, Product Type: Journal-Paper
Vol.10 , Issue.5 , pp.1-6, Oct-2023

Online published on Oct 31, 2023

Copyright © Anima Bag, Rojalini Patro . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

124 Views    169 Downloads    54 Downloads

Abstract :
The purpose of the paper is to develop an optimal strategy for the inventory system for perishable goods. Discount facility is adopted here for advanced payment. Demand is partially backlogged. Preservation technology is applied in the proposed model to reduce the rate of deterioration. An inventory model has been developed and the optimum order quantity as well as the time at which shortage occurs are determined which maximizes the total profit. To observe the practical utility of the proposed model, three numerical illustrations are provided which are solved by Mathematica 5.1 software. Concavity of the average profit is examined graphically. Finally a post optimality analysis is performed to show the effects of inventory parameters on optimal policy. The proposed model can be used for decaying items like fruits, vegetables, food grains and medicines that are subject to preservation technology to maximize the total profit.

Key-Words / Index Term :
Inventory, Decaying Items, Preservation Technology, Partial Backlogging, Advance Payment

References :
[1] A.K., Maiti, A.K. Bhunia, M. Maiti, “An application of real coded genetic algorithm (RCGA) for mixed integer non-linear programming in two-storage multi-item inventory model with discount policy”, Applied Mathematics and Computation. Vol.183, Issue2, pp 903–915, 2006.
[2] Anima Bag, P.K. Tripathy, “Decision support model with price and time induced demand under multilevel conditional deliveries” published in the journal, Investigacion operacional, Vol 40, Issue 4, pp 441-451, 2019.
[3] M.A. Khan, A.A. Shaikh,., G.C. Panda, I., Konstantaras, L.E. Ca´rdenas-Barro´n, “The effect of advance payment with discount facility on supply decisions of deteriorating products whose demand is both price and stock dependent”, International Transactions in Operational Research, Vol 27, Issue 3, pp1343–1367, 2020.
[4] A.Thangam, “Optimal price discounting and lot-sizing policies for perishable items in a supply chain under the advance payment scheme and two-echelon trade credits”, International Journal of Production Economics, Vol 139, Issue 2, pp 459–472, 2012.
[5] M.A. Khan, S. Ahmed, M.S. Babu, N. Sultana, “Optimal lot-size decision for deteriorating items with price-sensitive demand, Hybrid price and stock dependent inventory model for perishable goods with advance 3463 linearly time-dependent holding cost under all-units discount environment”, International Journal of Systems Science: Operations & Logistics Vol 9, Issue 2, pp 1–14, 2020.
[6] L.N. De, “A study of inventory model for deteriorating items with price and stock dependent demand under the joined effect of preservation technology and price discount facility”, Journal of Mathematics and Computer Science, Vol 10, Issue 5, pp 1481–1498, 2020.
[7] Q. Zhang, D. Zhang, Y.-C. Tsao, J. Luo, “Optimal ordering policy in a two-stage supply chain with advance payment for stable supply capacity”, International Journal of Production Economics, Vol 177, pp 34–43, 2016.
[8] R. Patro, M. Acharya, and M. M. Nayak, “An EOQ model for fuzzy defective rate with allowable proportionate discount”, Opsearch , Vol 26, Issue 1, pp 191-215, 2019.
[9] S. Sana, K.S. Chaudhuri, “A stock-review EOQ model with stock-dependent demand, quadratic deterioration rate”, Advanced Modeling and Optimization, Vol 6, Issue 2, pp 25–32, 2004.
[10] Z.T. Balkhi, L. Tadj, “A generalized economic order quantity model with deteriorating items and time varying demand, deterioration and costs”, International Transactions in Operational Research, Vol 15, Issue 4, pp 509–517, 2008.
[11] R. Maihami, I. Nakhai Kamalabadi, “Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand”, International Journal of Production Economics, Vol 136, Issue1, pp 116–122, 2012.
[12] A.A. Shaikh, G.C. Panda, S. Sahu, A.K. Das, “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, Vol 32, Issue 1, 2019.
[13] H. Hsu, H.M. Wee, H.M. Teng, “Preservation technology investment for deteriorating inventory”, International Journal of Production Economics, Vol 124 ,Issue 2, pp 388–394, 2010.
[14] Y.-P. Lee, C.-Y. Dye, “An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate”, Computer and Industrial Engineering, Vol 63, Issue 2, pp 474–482, 2012.
[15] Q. Zhang, Y.-C. Tsao, T.-H. Chen, “Economic order quantity under advance payment”, Applied Mathematical Modeling, Vol 38 , Issue 24, pp 5910–5921, 2014.
[16] U. Mishra, L.E. Ca´rdenas-Barro´n, S. Tiwari, A.A. Shaikh, G. Trevin˜o-Garza, “An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment”, Annals of Operations Research, Vol 254 (1-2), pp165–190, 2017.
[17] C.-T. Yang, C.-Y. Dye, J.-F. Ding, “Optimal dynamic trade credit and preservation technology allocation for a deteriorating inventory model”, Computer and Industrial Engineering, Vol 87, pp 356–369, 2015.
[18] Q. Zhang, D. Zhang, Y.-C. Tsao, J. Luo, “Optimal ordering policy in a two-stage supply chain with advance payment for stable supply capacity”, International Journal of Production Economics, Vol. 177, pp. 34–43, 2016.
[19] U. Mishra, L.E. Ca´rdenas-Barro´n, S. Tiwari, A.A. Shaikh, G. Trevin˜o-Garza, “An inventory model under price and stock dependent demand for controllable deterioration rate with shortages and preservation technology investment”, Annals of Operations Research, Vol 254 (1-2), pp. 165–190, 2017.
[20] S.C. Das, A.M. Zidan, A.K. Manna, A.A. Shaikh, A.K. Bhunia, “An application of preservation technology in inventory control system with price dependent demand and partial backlogging”, Alexandria Engineering Journal, Vol. 59(3), pp.1359-1369, 2020.
[21] H.L. Yang, J.T. Teng, M.S. Chern, “ An inventory model under inflation for deteriorating items with stock-dependent consumption rate and partial backlogging shortages”, International Journal of Production Economics, Vol 123, Issue1, pp 8–19, 2010.
[22] P.K. Tripathy, A.Bag, “Optimal disposal strategy with controllable deterioration and shortage” published in the journal, International Journal of Agricultural and Statistical Sciences, Vol. 15,Issue1, pp 271-279, 2019.
[23] A. Bag, P.K. Tripathy, “Decision support model with price and time induced demand under multilevel conditional deliveries” published in the journal, Investigacion operacional, Vol. 40, Number 4, pp. 441-451, 2019.
[24] P.K. Tripathy, A. Bag, “Decision support model with default risk under conditional delay” published in the journal, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 5, Issue 2, pp. 40-45, 2018.
[25] R. Patro, M. Acharya, M. M. Nayak, and S. Patnaik, “A fuzzy inventory model with time dependent weibull deterioration, quadratic demand and partial backlogging”, International Journal of Management and Decision Making, Vol.16, Issue3, pp. 243-279, 2017.