A Magnitude Ranking Approach for a Green Inventory Model with Carbon Tax and Carbon Cap and Trade Policies Under Uncertainty

Abstract

Abating carbon emission which is emitted from manufacturing sectors and organizations is the important act to be performed at present to safeguard our environment. So to dwindle such emissions, in the last couple of decades both government and sectors are focusing on it by implementing new techniques and policies. Carbon tax and Carbon cap and trade are the two policies initiated at present by many firms and discussed by researchers in production inventory system. Most importantly facing unpredictability among parameters in a green EOQ model is the most efficient need in today’s scenario of changing life condition and technical advancement among customers. So this model concentrates in a way to remove ambiguity in few parameters through fuzzy idea by considering them as trapezoidal fuzzy numbers. The optimal solution is found by using magnitude ranking method. Numerical example is given to illustrate the model.

Introduction

Global warming, driven mainly by industrial carbon emissions, poses serious environmental and societal risks. To curb these emissions, regulatory bodies have implemented carbon policies like carbon tax and carbon cap-and-trade.

• Carbon tax charges a fee per unit of CO2 emitted, increasing companies’ operational costs proportional to their emissions.

• Carbon cap-and-trade sets a limit on emissions; firms that emit less can sell unused allowances, while those exceeding limits must buy extra permits.

Green inventory management integrates these carbon policies to help industries reduce emissions while maintaining economic viability. Various researchers have developed production-inventory models incorporating carbon regulations and green technologies to optimize supply chain performance.

Due to uncertainties in demand, production rates, costs, and emissions, fuzzy logic methods are applied to handle such vagueness. Specifically, trapezoidal fuzzy numbers and magnitude ranking techniques help model uncertain parameters and derive optimal order quantities and costs under carbon policies.

Key aspects include:

• Integrated two-tier vendor-buyer supply chain with variable demand and uncertain parameters.

• Models developed for both carbon tax and carbon cap-and-trade policies with crisp and fuzzy data.

• Fuzzy parameters enable better handling of real-world uncertainties.

• Mathematical formulations derive optimal order quantities minimizing total costs, including carbon-related expenses.

Numerical examples illustrate how the fuzzy green inventory model calculates optimal orders and costs under both carbon policies, demonstrating its practical application in sustainable supply chain management.

Conclusion

In the global environment, uncertainty exists everywhere making or creating a path to rectify it. This study considered a green inventory model under two policies and implemented magnitude ranking defuzzification approach by considering certain parameters with ambiguous nature as trapezoidal fuzzy numbers. Comparison of crisp and fuzzy perspective solutions is performed for both cases which helps to identify the effectiveness of fuzzy idea in green inventory system. Here it is observed that the fuzzy optimum order quantity under two cases provides same result but slightlythat is 0.32 size lower than crisp order quantity. And fuzzy optimum total cost in two cases differs but most importantly compared to crisp results it gets reduced and thus resulting in minimized total expenses. Hence this research work proves the advantage of fuzzy frame work in supply chain especially with sustainable features.

References

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Copyright

Copyright © 2025 Alda. W. S., Rexlin Jeyakumari S.. 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.