Deteriorating inventory under carbon cap-and-trade: profit–emission trade-offs between no-shortage and backlogging policies

Zhonghui Li; Panida Chamchang; Wipada Sompong; Lili Niu; Zhonghui Li; Panida Chamchang; Wipada Sompong; Lili Niu

doi:10.3934/math.20261164

AIMS Mathematics

2026, Volume 11, Issue 9: 29285-29311. doi: 10.3934/math.20261164

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Deteriorating inventory under carbon cap-and-trade: profit–emission trade-offs between no-shortage and backlogging policies

1.
College of Mathematics and Quantitative Economics, Guangxi University of Finance and Economics, Nanning 530003, China
2.
College of Graduate Studies, Walailak University, Nakhon Si Thammarat 80160, Thailand
3.
Department of Logistics Management, School of Management, Walailak University, Nakhon Si Thammarat 80160, Thailand
4.
Guangxi Agricultural Vocational and Technical University, Nanning 530009, China

Received: 23 April 2026 Revised: 01 August 2026 Accepted: 17 August 2026 Published: 11 September 2026
MSC : 90B06, 90C90

This study investigated profit–emission trade-offs in deteriorating inventory systems under a carbon cap-and-trade mechanism with exponentially time-varying demand and a constant deterioration rate. Two profit-maximizing models were developed for a retailer: a no-shortage policy and a complete backlogging policy. The analysis established the existence and uniqueness of the optimal replenishment decisions, including the replenishment cycle, order quantity, and shortage interval where applicable. Numerical results showed that, compared with systems without carbon regulation, both models reduce carbon emissions per unit time under the cap-and-trade mechanism, confirming its operational effectiveness. The results further indicate that the complete backlogging policy yields higher profits, but it also produces higher emissions and greater sensitivity to key cost parameters. In particular, shortage cost plays an important role in balancing profitability and environmental performance. These findings provide practical guidance for designing sustainable inventory strategies un-der carbon cap-and-trade regulation.
- carbon cap-and-trade,
- backlogging policy,
- deteriorating inventory,
- profit-emission trade-off,
- low carbon inventory management
Citation: Zhonghui Li, Panida Chamchang, Wipada Sompong, Lili Niu. Deteriorating inventory under carbon cap-and-trade: profit–emission trade-offs between no-shortage and backlogging policies[J]. AIMS Mathematics, 2026, 11(9): 29285-29311. doi: 10.3934/math.20261164

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Abstract

This study investigated profit–emission trade-offs in deteriorating inventory systems under a carbon cap-and-trade mechanism with exponentially time-varying demand and a constant deterioration rate. Two profit-maximizing models were developed for a retailer: a no-shortage policy and a complete backlogging policy. The analysis established the existence and uniqueness of the optimal replenishment decisions, including the replenishment cycle, order quantity, and shortage interval where applicable. Numerical results showed that, compared with systems without carbon regulation, both models reduce carbon emissions per unit time under the cap-and-trade mechanism, confirming its operational effectiveness. The results further indicate that the complete backlogging policy yields higher profits, but it also produces higher emissions and greater sensitivity to key cost parameters. In particular, shortage cost plays an important role in balancing profitability and environmental performance. These findings provide practical guidance for designing sustainable inventory strategies un-der carbon cap-and-trade regulation.

References

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