Optimal control approach for solving a supply chain problem under variable demand and emissions tax regulation with an unknown production rate

Supply chains and other complex systems can be effectively managed and optimised with the help of optimal control techniques. Optimal control, as used in supply chain management, is the process of using mathematical optimisation techniques to identify the best course of action for controlling a given objective function over time. Modeling the supply chain's dynamics, which include elements like production rates, inventory levels, demand trends, and transportation constraints, is the best control strategy when applied to a supply chain. In this study, we have considered that production rate is an unknown function of time, which is a controlling function. The demand for the product is taken as a function of price and time. The emission of carbon is taken as a linear function of the production rate of the system. To solve the suggested supply chain system, we have used an optimal control approach for determining the unknown production rate. To find the optimal values of the objective function as well as the decision variables, we have used different meta-heuristic algorithms and compared their results. It is observed that the equilibrium optimizer algorithm performed better than other algorithms used. Finally, a sensitivity analysis is performed, which is presented graphically in order to choose the best course of action.