Supply chains face increasing complexity as companies struggle to balance profitability, fluctuating market demand, and carbon emission regulations. Researchers from The University of Burdwan, Jahangirnagar University and Tecnologico de Monterrey have developed an optimal control-based supply chain model that addresses these challenges by treating production rate as an unknown time-dependent variable rather than a fixed value.
The work, published in Frontiers of Engineering Management in 2025, introduces an approach where production rate is adjusted dynamically as an unknown time-dependent function. The model integrates price- and time-sensitive demand for both retailers and consumers, linking carbon emission levels directly to production intensity. Using metaheuristic algorithms to solve the model, the researchers identified the Equilibrium Optimizer Algorithm (EOA) as the most effective method for determining optimal production decisions.
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 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. 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 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 complete research is available at https://doi.org/10.1007/s42524-025-4110-6.
