An Economic Production Quantity Model Approach by Lowering the Impact of Carbon Emission under Uncertain Environment

Abstract

The primary factor of rising global temperatures is the increase in carbon dioxide emissions, which have serious consequences on both ecological and social well-being worldwide. It contributes to environmental damage and poses various health hazards to society. This study aims to develop a fuzzy economic production quantity model with emission reduction strategies to promote economic profitability and ecological sustainability in inventory functions. Two models were developed: the fuzzy model and the crisp model. The parameters in this research work are taken as trapezoidal fuzzy numbers. The Yager ranking method and beta distribution methods are used for the solution procedure. A numerical example is used for a better understanding of the research work.

Introduction

As global warming intensifies, governments and industries are emphasizing carbon emission reduction throughout production and inventory processes. Strategies include carbon taxes, recycling initiatives, emission limits, and green investments. Recycling is especially valued for its role in reducing pollution and conserving natural resources.

Background and Related Work

Several researchers have developed sustainable inventory models that include factors like:

• Carbon emissions from production, transportation, storage, and waste disposal

• The impact of green investments

• Use of machine learning and fuzzy logic for uncertainty handling

Fuzzy set theory, which models imprecision and ambiguity, is used to manage uncertainty in parameters like cost, demand, and recycling rates.

Research Focus

This study proposes a manufacturing inventory model that incorporates:

• Recycling processes

• Green technology investment

• Carbon taxation

• Fuzzy uncertainty modeling using trapezoidal fuzzy numbers

Two fuzzy decision-making methods are applied:

1. Yager Ranking Method

2. Beta Distribution Method

Model Details

1. Crisp (Deterministic) Model

• Includes carbon emissions from production, shipping, warehousing, waste disposal, and recycling.

• Calculates total inventory cost using conventional formulas.

• Optimizes order quantity by minimizing total cost.

2. Fuzzy Model

• Uncertain parameters (costs, rates, emissions) are modeled as trapezoidal fuzzy numbers.

• Total inventory cost and optimal order size are derived using two fuzzy methods:

  • Yager Ranking Approach

  • Beta Distribution Method

Key Definitions

• Fuzzy Set: Represents uncertain values with degrees of membership.

• Trapezoidal Fuzzy Number: Used to model uncertainty in parameters.

• Alpha Cut: Set of values that belong to a fuzzy set at a certain confidence level.

• Yager Ranking: Ranks fuzzy numbers for decision-making.

• Beta Distribution: Defuzzifies fuzzy numbers using a probability distribution.

Mathematical Model

• Formulates total cost equations incorporating fuzzy variables.

• Derives formulas for optimal order quantity in both crisp and fuzzy settings.

Numerical Example

• Crisp and fuzzy parameter values are used to compute:

  • Total inventory cost

  • Optimal order size

Results:

• Crisp model gives fixed order quantity and cost.

• Fuzzy models (using Yager and Beta methods) provide slightly different optimal values due to uncertainty modeling.

Conclusion

Recycling is indispensable for the advancement of environmental preservation in a number of ways.On an economic scale, it lowers the systematic consumption of essential resources, ultimately resulting in cost savings.It has an advantageous ecological influence through reducing CO2 emissions and solid waste generation. This paper developed economic manufacturing model with ecological concerns of lowering emissions by adopting recycling and green technology investment in inventory functions.The findings of the research suggest that the Yager ranking method provides a lower solution results than beta distribution method.

References

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Copyright

Copyright © 2025 V Vinola Elisabeth, S Rexlin Jeyakumari. 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.