Supply chains worldwide face mounting pressure from fluctuating market demands and increasingly stringent carbon emission regulations, creating complex challenges for manufacturers seeking both profitability and sustainability. A new study published in Frontiers of Engineering Management presents an optimal control-based model that addresses these dual pressures by treating production rate as a dynamic variable rather than a fixed parameter. The research, available at https://doi.org/10.1007/s42524-025-4110-6, demonstrates how adaptive production strategies can reduce environmental impact while improving coordination between manufacturers and retailers.
The study's importance lies in its practical approach to a critical business dilemma: how to maintain economic viability while complying with global carbon tax policies. As governments worldwide implement emission regulations to curb greenhouse gases, production systems face additional operational pressures that traditional supply chain models fail to address. Most existing studies assume constant production rates, overlooking real-world fluctuations and their environmental consequences. This research fills that gap by integrating price- and time-dependent demand with emission policies, offering industries a more realistic framework for decision-making.
Researchers from The University of Burdwan, Jahangirnagar University, and Tecnologico de Monterrey developed 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 this non-linear variational problem, the researchers applied optimal control theory and evaluated decentralized scenarios using Stackelberg game analysis.
The study's methodology involved testing six metaheuristic algorithms to obtain optimal decisions for production, pricing, inventory, and emission costs. These included the Artificial Electric Field Algorithm, Firefly Algorithm, Grey Wolf Optimizer, Sparrow Search Algorithm, Whale Optimizer Algorithm, and the Equilibrium Optimizer Algorithm (EOA). Results showed that EOA outperformed other algorithms in solution accuracy, convergence, and stability. Sensitivity analysis further demonstrated how variations in tax rate, production cost, or price elasticity influence profit and emission outcomes.
This research provides a decision-support framework for industries operating under carbon regulation policies, particularly relevant for sectors like 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 model's ability to dynamically adjust production in response to demand and emission constraints represents a significant advancement toward sustainable and economically viable supply chain operations.
