Researchers have developed a novel supply chain model that addresses the dual challenges of fluctuating market demand and increasing carbon emission regulations by treating production rate as a dynamic variable rather than a fixed constant. The study, published in Frontiers of Engineering Management in 2025, demonstrates how this approach can reduce emissions while improving coordination between manufacturers and retailers, offering a practical path toward sustainable and economically viable supply chain operations. Modern supply chains operate under volatile demand influenced by seasonality, price changes, and consumer behavior, making coordination between manufacturers and retailers difficult. Meanwhile, governments globally are enforcing carbon taxes to curb greenhouse emissions, further increasing operational pressure on production systems.
Most existing supply chain studies assume constant production rates, overlooking real-world fluctuations and their environmental consequences. The new model addresses this gap by integrating price- and time-dependent demand with emission policies while considering production rate as an unknown control function. The research, conducted by teams from The University of Burdwan, Jahangirnagar University and Tecnologico de Monterrey, formulates a two-layer manufacturer–retailer supply chain model where market demand depends simultaneously on selling price and time. Production rate is defined as a control variable, and carbon emission is modeled as a linear function of production intensity—meaning higher production generates proportionally higher emissions.
To solve the non-linear variational problem, the researchers applied optimal control theory and further evaluated decentralized scenarios using Stackelberg game analysis. To obtain optimal decisions for production, pricing, inventory, and emission costs, six metaheuristic algorithms were tested and compared. The results show that the Equilibrium Optimizer Algorithm (EOA) outperformed other algorithms in solution accuracy, convergence, and stability. Sensitivity analysis further demonstrates how variations in tax rate, production cost, or price elasticity influence profit and emission outcomes. These findings confirm that dynamic production control can reduce environmental impact while maintaining profitability—offering a more realistic strategy than models using fixed production assumptions.
This model brings production planning closer to real industry conditions. By treating production rate as a variable instead of a constant, we allow the system to react to demand and emission constraints over time. Through optimal control and algorithmic optimization, manufacturers can identify profitable operational levels without compromising environmental goals. The complete study is available at https://doi.org/10.1007/s42524-025-4110-6. This research provides a decision-support framework for industries operating under carbon regulation policies. It can guide manufacturers in adjusting production dynamically to balance cost, demand fluctuation, and emission targets.
The model is applicable to sectors such as steel, cement, chemicals, consumer goods, and logistics—where carbon output scales directly with production intensity. With global emission taxes tightening, this approach may help companies develop greener strategies, lower penalties, and improve collaboration with retailers. Future work could incorporate stochastic events, renewable energy inputs, or multi-product chains to further enhance sustainability-driven supply chain design.
