Supply chains face increasing complexity as companies struggle to balance profitability, fluctuating market demand, and carbon emission regulations. A new study published in Frontiers of Engineering Management in 2025 develops an optimal control-based supply chain model in which production rate is treated as an unknown time-dependent variable rather than a fixed value. This approach offers 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.
Researchers from The University of Burdwan, Jahangirnagar University and Tecnologico de Monterrey reported a new optimal control-based model that addresses supply chain coordination under variable demand and carbon emission tax conditions. The work, published with DOI 10.1007/s42524-025-4110-6 in Frontiers of Engineering Management, introduces an approach where production rate is not fixed but adjusted dynamically as an unknown time-dependent function.
The study 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, including the Artificial Electric Field Algorithm, Firefly Algorithm, Grey Wolf Optimizer, Sparrow Search Algorithm, Whale Optimizer Algorithm, and the Equilibrium Optimizer Algorithm (EOA). The results show that 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," the authors explain. "By treating production rate as a variable instead of a constant, we allow the system to react to demand and emission constraints over time."
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.
The implications of this research extend across industries facing carbon tax pressures. As governments worldwide implement stricter emission regulations, companies must find ways to remain profitable while reducing their environmental footprint. This model offers a mathematical framework that could transform how supply chains are managed, potentially reducing carbon emissions across manufacturing sectors while maintaining economic viability. Future work could incorporate stochastic events, renewable energy inputs, or multi-product chains to further enhance sustainability-driven supply chain design.
