Inventory Model for Non-Instantaneous Deteriorating Items with Stock-Dependent Demand and Preservation Technology Investment

Anwesha  Samanta; Manisha  Pal

Authors

Anwesha Samanta School of Mathematics, Applied Statistics and Analytics, NMIMS, India
Manisha Pal Department of Statistics, St. Xavier’s University, Faculty of Science, Kolkata, India

Keywords:

Non-instantaneous and time dependent deterioration, waiting time dependent backlogging, preservation cost, cost optimization

Abstract

The paper considers an inventory system for non-instantaneous deteriorating items when demand is dependent on the stock level. Time dependent deterioration and partial waiting time dependent backlogging rates are assumed to model the inventory system. Deterioration, although non-instantaneous, is not desirable. Hence some technique that can reduce deterioration is very necessary. However, that will involve a certain amount of cost. This preservation technology investment and its effect on the inventory decision are considered in this paper. The optimum cost function is formulated, and its convexity is proven. The study is supported by hypothetical illustrations that suggest that the minimum cost decreases owing to the preservation technology adopted. Managerial aspects, future scope and the limitations of the study are also discussed alongside the findings and conclusions. It is concluded that although preservation technology involves certain amount of investment, the total cost is reduced by its application.

References

Bardhan S, Pal H, and Giri BC. Optimal replenishment policy and preservation technology investment for a non-instantaneous deteriorating item with stock-dependent demand. Oper Res-Ger. 2019; 19(2): 347-368.

Benkherouf L, Balkhi ZT. On an inventory model for deteriorating items and time-varying demand. Math Method Oper Res. 1997; 45(2): 221-233.

Chakrabarty T, Giri BC, Chaudhuri KS. An EOQ model for items with Weibull distribution deterioration. shortages and trended demand: an extension of Philip's model. Comp Oper Res. 1998; 25(7-8): 649-657.

Covert RP, Philip GC. An EOQ Model for Items with Weibull distribution deterioration. AIIE Transactions. 1973; 5(4): 323-326.

De LN. 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. J Math Comput Sci. 2020; 10(5): 1481-1498.

Dye CY. The effect of preservation technology investment on a non-instantaneous deteriorating inventory model. Omega. 2013; 41(5): 872– 880.

Dye CY, Hsieh TP. An optimal replenishment policy for deteriorating items with effective investment in preservation technology. Eur J Oper Res. 2012; 218(1): 106-112.

Geetha KV, Udayakumar R. Optimal lot sizing policy for non-instantaneous deteriorating items with price and advertisement dependent demand under partial backlogging. Int J Appl Comput Math. 2016; 2: 171-193.

Ghare PM, Scharder GF. A model for exponentially decaying inventory systems. J Ind Engineering. 1963; 14: 238-243.

Giri BC, Pal H, Maiti T. A vendor-buyer supply chain model for time-dependent deteriorating item with preservation technology investment. Int J Math Oper Res. 2017; 10(4): 431-449.

He Y, Huang, H. Optimizing inventory and pricing policy for seasonal deteriorating products with preservation technology investment. J Ind Eng. 2013, https://doi.org/10.1155/2013/793568

Hsu PH, Wee HM, Teng HM. Preservation technology investment for deteriorating inventory. Int J Prod Econ. 2010; 124: 338-394.

Khanna A, Pritam P, Jaggi CK. Optimizing preservation strategies for deteriorating items with time-varying holding cost and stock-dependent demand. Yugoslav J Oper Res. 2020; 30(2): 237-250.

Lee YP, Dye CY. An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate. Comp Ind Eng. 2012; 63(2): 474-482.

Mahata S, Debnath BK. A profit maximization single item inventory problem considering deterioration during carrying for price dependent demand and preservation technology investment. RAIRO Oper Res. 2022; 56(3): 1841-1856.

Maihami R, Abadi INK. Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging. Math Comput Model. 2012a; 55(5-6): 1722-1733.

Maihami R, Abadi INK. Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand. Int J Prod Econ. 2012b; 136(1): 116-122.

Mishra U, Tijerina-Aguilera J, Tiwari S, Cárdenas-Barrón LE. Retailer’s joint ordering, pricing, and preservation technology investment policies for a deteriorating item under permissible delay in payments. Math Probl Eng. 2018.

Ouyang LY, Wu KS, Yang CT. A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments. Comp Ind Eng. 2006; 51(4): 637-651.

Philip GC. A generalized EOQ model for items with Weibull distribution deterioration. AIIE Transactions. 1974; 6(2):159-162.

Sarkar B, Sarkar S. An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand. Econ Model. 2013; 30: 924-932.

Shah NH, Soni HN, Patel KA. Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates. Omega. 2013; 41(2): 421-430.

Singh SR, Khurana, D, Tayal S. An economic order quantity model for deteriorating products having stock dependent demand with trade credit period and preservation technology. Uncertain Supply Chain Manag. 2016; 4(1): 29-42.

Skouri K, Papachritos S. Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging. Int J Prod Econ. 2003; 81-82: 525-531.

Tadikamalla PR. An EOQ inventory for items with gamma distributed deterioration. AIIE Transactions. 1978; 10(1): 100-103.

Tsao YC, Sheen GJ. Joint pricing and replenishment decisions for deteriorating items with lot-size and time-dependent purchasing cost under credit period. Int J Syst Sci. 2007; 38(7): 549-561.

Wee HM. A replenishment policy for items with a price-dependent demand and a varying rate of deterioration. Prod Plan Control. 1997; 8(5): 494-499.

Wu KS, Ouyang LY, Yang CT. An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. Int J Prod Econ. 2006; 101(2): 369-384.

Zhang J, Bai Z, Tang W. Optimal pricing policy for deteriorating items with preservation technology investment. J Ind Manag Optim. 2014; 10(4): 1261-1277.