Optimal Control Policy of Unreliable Production Systems Generating Greenhouse Gas Emission

The current paper addresses the production planning problem of unreliable manufacturing systems generating greenhouse gas (GHG) emissions, producing a single product type in a dynamic and stochastic context. This work aims to develop a control policy that minimizes the sum of backlog, inventory, and emission costs. To achieve this goal, the stochastic optimal control theory is used to develop the optimality conditions solved by numerical techniques to establish the control policy structure. Sensitivity analyses are provided to depict and validate the obtained structure of the production policy characterized by multiple thresholds, which regulate the production rate with the emission and inventory levels. Furthermore, the performance of the developed optimal control policy is compared with the most pertinent ones identified in the literature. The developed optimal control policy outperformed those in the literature by significantly reducing the total cost incurred by these policies. Finally, the developed control policy is implemented to equip the manager of the considered manufacturing system with a practical and robust decision-support tool.