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

Year : 2026 | Volume : 04 | Issue : 01 | Page : 20 28
    By

    Sanjay Kumar Behera,

  • Chandan Kumar Sahoo,

  • Kailash Chandra Paul,

  1. Research Scholar, Department of Mathematics, BPUT, Raurkela, Odisha, India
  2. Assistant Professor, Dept of Mathematics, Gandhi Institute of Excellent Technocrat, Odisha, India
  3. Assistant Professor, Dept of Mathematics, IGIT Saranga, Odisha, India

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: Deteriorating items, demand, partial Backlogging, carbon Emission

[This article belongs to International Journal of Industrial and Product Design Engineering ]

How to cite this article:
Sanjay Kumar Behera, Chandan Kumar Sahoo, Kailash Chandra Paul. A Sustainable EOQ Model for Declining Products Incorporating Cubic Demand, Variable Deterioration, Partial Backlogging, and Carbon Emission Optimization. International Journal of Industrial and Product Design Engineering. 2026; 04(01):20-28.
How to cite this URL:
Sanjay Kumar Behera, Chandan Kumar Sahoo, Kailash Chandra Paul. A Sustainable EOQ Model for Declining Products Incorporating Cubic Demand, Variable Deterioration, Partial Backlogging, and Carbon Emission Optimization. International Journal of Industrial and Product Design Engineering. 2026; 04(01):20-28. Available from: https://journals.stmjournals.com/ijipde/article=2026/view=239617


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Regular Issue Subscription Review Article
Volume 04
Issue 01
Received 22/01/2026
Accepted 10/02/2026
Published 14/02/2026
Publication Time 23 Days
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