Abstract
The transition toward low-carbon supply chains requires inventory policies that jointly consider economic performance, service reliability and environmental impact. This study develops an integrated green inventory optimization framework for a two-echelon supply chain under stochastic demand and carbon cap-and-trade regulation. The model jointly determines order quantity, safety stock and green-technology investment while accounting for ordering, holding, production, transportation, shortage, green-investment and carbon-regulation costs. Carbon emissions are decomposed into production, transportation and inventory-holding components, and green investment reduces emission intensity through a diminishing-returns function. Demand uncertainty is represented through a service-level-based safety-stock formulation. A normalized multi-objective function balances economic cost against carbon emissions. Because the resulting nonlinear constrained problem is non-convex when regulatory penalties and investment effects are combined, a hybrid GWO–PSO–LS algorithm is developed. GWO supplies population-level exploration, PSO accelerates movement toward promising regions, and local search refines elite solutions. An illustrative computational experiment using reproducible synthetic parameters compares the proposed method with GWO, PSO and Differential Evolution. The results demonstrate the computational behavior and the economic–environmental trade-off of the proposed framework without representing the synthetic outcomes as empirical industry observations. The manuscript concludes with sensitivity analysis, managerial implications and directions for incorporating robust, data-driven and multi-product extensions.
Introduction
Inventory decisions have traditionally been evaluated through ordering, holding, purchasing and shortage costs. However, contemporary supply chains operate under environmental constraints that make production, transportation and storage decisions inseparable from carbon performance. A replenishment policy can reduce ordering frequency while increasing average inventory, whereas a smaller lot size can reduce holding-related emissions at the expense of more frequent transportation. Consequently, green inventory management is fundamentally a trade-off problem rather than a simple extension of the classical EOQ model.
Recent research confirms that sustainable inventory management has evolved toward carbon regulation, green investment, deterioration control, uncertainty and metaheuristic optimization. A 2025 taxonomy and literature review classified a large body of sustainable inventory studies under carbon-tax, carbon-cap, cap-and-trade and cap-and-offset mechanisms and identified uncertainty, real-world validation and soft-computing approaches as important future directions [1]. Recent 2026 work has further integrated green investment, preservation technology and carbon cap-and-trade regulation with metaheuristic optimization [2], while other 2026 studies examine carbon-sensitive inventory decisions and sustainable inventory systems under variable demand [3,4].
The present study responds to this direction by combining stochastic demand, safety stock, green investment and carbon cap-and-trade within one integrated inventory framework. The computational contribution is a hybrid GWO–PSO–LS procedure designed for the resulting nonlinear optimization problem. The emphasis is not on claiming that carbon regulation or metaheuristics are new individually; instead, novelty is pursued through the particular integration of economic, service and environmental decisions and through an explicit reproducible hybrid search architecture.
Conclusion
This study develops an integrated green inventory optimization framework for a two-echelon supply chain operating under stochastic demand and carbon cap-and-trade regulation. The model links replenishment quantity, safety stock, green investment and carbon emissions within a unified economic–environmental objective. Production, transportation and inventory-holding emissions are modeled explicitly, while green investment reduces emission intensity with diminishing returns. A hybrid GWO–PSO–Local Search algorithm is proposed to address the nonlinear decision problem. The synthetic computational experiment demonstrates how the methodology can be implemented and compared with established metaheuristics without presenting fabricated industry evidence. The main conceptual finding is that sustainable inventory policy is inherently a trade-off among service protection, shipment frequency, inventory exposure, carbon regulation and green investment. The framework therefore provides a foundation for future data-driven and robust green inventory studies. Acknowledgements The authors gratefully acknowledge the financial support provided by the Government of Uttar Pradesh under Letter No. 24/2023/681/Sattar-4-2023-002-4(59)/2022. The authors sincerely thank the Government of Uttar Pradesh for supporting this research project and facilitating the successful completion of the work. The authors also gratefully acknowledge the valuable contribution of Mr. Vikas Kumar, Research Associate, for his dedicated involvement in the research project, constructive academic inputs, assistance in the research activities, critical review, and valuable suggestions that contributed significantly to the development and refinement of this work.
References
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2025