STM Journals Peer-reviewed research from Consortium e-Learning Network

International Journal of Industrial and Product Design Engineering Review Article

A Sustainable EOQ Model for Declining Products Incorporating Cubic Demand, Variable Deterioration, Partial Backlogging, and Carbon Emission Optimization

  1. Sanjay Kumar Behera Department of Mathematics, BPUT, Raurkela
  2. Chandan Kumar Sahoo Dept of Mathematics, Gandhi Institute of Excellent Technocrat
  3. Kailash Chandra Paul Dept of Mathematics, IGIT Saranga

Abstract

In this paper proposes a sustainable Economic Order Quantity (EOQ) model for inventory systems involving decaying items under cubic time-dependent demand, variable decaying rates, and partial backlogging while absolutely considering carbon emission costs. The model reflects practical market actions where demand initially increases and afterwards declines over time, and decay depends on the age of the item. To demonstrate the current model's applicability as well as evaluate the trade-off between economic and environmental goals, a numerical example is given. The research results emphasize how crucial it is to bring in ecological factors into inventory planning, thus providing valuable information for companies looking for sustainable and affordable methods for handling their stocks. Furthermore, the proposed framework integrates holding costs, ordering costs, deterioration costs, shortage costs, and emission-related penalties into a unified total cost function, which is minimized to determine the optimal replenishment cycle and order quantity. The mathematical formulation is developed using differential equations to capture the dynamic nature of inventory depletion over time. Sensitivity analysis is also conducted to examine the influence of key parameters such as deterioration rate, carbon tax rate, demand coefficients, and backlogging fraction on the optimal solution. The findings reveal that stricter carbon regulations and higher emission costs significantly impact replenishment decisions and encourage environmentally responsible inventory policies. The model offers managerial insights for industries dealing with perishable or fast-moving goods, enabling decision-makers to balance profitability with sustainability objectives in an increasingly carbon-conscious economic environment.

Keywords

References (20)

  1. Chung K. and Ting P., 1993, An heuristic for replenishment of deteriorating items with a linear trend in demand; Journal of the Operational Research Society, 44, 1235–1241.
  2. Covert R. P., and Philip G. C., 1973, An EOQ model for items with Weibull distribution deterioration; AIIE Transactions, 5, 323–326.
  3. C. Philip, “A Generalized EOQ Model for Items with Weibull Distribution,” AIIE.
  4. Chang HJ, Dye CY. An EOQ model for deteriorating items with time varying demand and partial backlogging. Journal of the Operational Research Society. 1999;50(11):1176-1182. doi:10.1057/palgrave.jors.2600801
  5. Hui-Ming Wee. A deterministic lot-size inventory model for deteriorating items with shortages and a declining market. Computers & Operations Research. 1995;22(3):345-356. doi:10.1016/0305-0548(94)e0005-r
  6. Wee HM. Joint pricing and replenishment policy for deteriorating inventory with declining market. International Journal of Production Economics. 1995;40(2-3):163-171. doi:10.1016/0925-5273(95)00053-3
  7. Ouyang LY, Wu KS, Cheng MC. An inventory model for deteriorating items with exponential declining demand and partial backlogging. Yugoslav Journal of Operations Research. 2005;15(2):277-288. doi:10.2298/yjor0502277o
  8. Hariga MA, Benkherouf L. Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand. European Journal of Operational Research. 1994;79(1):123-137. doi:10.1016/0377-2217(94)90400-6
  9. M. Ghare and G. H. Schrader, “A Model for Exponentially Decaying Inventory Systems,” International Journal of Production and Research, Vol. 21, 1963, pp. 449–460.
  10. Covert RP, Philip GC. An EOQ Model for Items with Weibull Distribution Deterioration. A I I E Transactions. 1973;5(4):323-326. doi:10.1080/05695557308974918
  11. HOLLIER RH, MAK KL. Inventory replenishment policies for deteriorating items in a declining market. International Journal of Production Research. 1983;21(6):813-836. doi:10.1080/00207548308942414
  12. Sachan RS. On (T, Si) Policy Inventory Model for Deteriorating Items with Time Proportional Demand. Journal of the Operational Research Society. 1984;35(11):1013-1019. doi:10.1057/jors.1984.197
  13. Goyal SK, Giri BC. Recent trends in modeling of deteriorating inventory. European Journal of Operational Research. 2001;134(1):1-16. doi:10.1016/s0377-2217(00)00248-4
  14. Sahoo N. K., Sahoo C. K. and Sahoo S. K., 2009 An EOQ model with two parameter constant deterioration and price dependent demand; International Journal of Ultra Scientist of Physical Sciences, 21(2) M 515-520.
  15. P. Aggarwal, “A Note on an Order-Level Model for a System with Constant Rate of Deterioration,”Opsearch, Vol. 15, No. 4, 1978, pp. 184-187.
  16. Dave U, Patel LK. (T, Si) Policy Inventory Model for Deteriorating Items with Time Proportional Demand. Journal of the Operational Research Society. 1981;32(2):137-142. doi:10.1057/jors.1981.27
  17. K. Shah and M. C. Jaiswal, “An Order-Level Inventory Model for a System with Constant Rate of Deterioration,” Opsearch, Vol. 14, No. 3, 1977, pp. 174-184.
  18. Sahoo CK, Paul KC, Kalam A. An EOQ representation for declining matters with cubic order, inconsistent declination and inequitable backlogging. AIP Conference Proceedings. 2020;2253:020010. doi:10.1063/5.0018991
  19. C. K and Paul. K.C. (2021), An EOQ model for cubic degrading substances promoted keeping Weibull requisition and lacking scarcity.
  20. Paul KC, Sahoo CK, Sarangi MR. An Optimal Policy with Parabolic Demand Carry Forwarded with Three-Parameter Weibull Distribution Deterioration Rate, Scarcity and Salvage Value. Advances in Sustainability Science and Technology. 2022:29-46. doi:10.1007/978-981-19-2277-0_3