Dual-mode production planning for manufacturing with emission constraints

• We model a dual-mode production planning problem for manufacturing with two types of emission constraints.
• The structure of the model is carefully investigated and some analytical properties are proven.
• The subproblem of choosing the optimal mix of production modes is addressed.
• A polynomial dynamic programming algorithm is developed to solve the problem optimally.

We study a dual-mode production planning problem with emission constraints, where a manufacturer produces a single product with two optional technologies. The manufacturer is equipped with the regular and green technologies to comply with emission limitations, and either one or both can be adopted for production. We first investigate the problem under a mandatory emission-cap policy and then extend it to consider emission trading under an emission cap-and-trade scheme. Based on the structural properties of the problem and a multi-level decomposition approach, a polynomial dynamic programming algorithm is developed to solve the models optimally. Our analysis shows that the manufacturer should only use a mix of both technologies when the emission cap is a binding constraint. Numerical results show that the manufacturer’s decisions and benefits are significantly affected by the emission cap under the mandatory emission-cap policy, especially when the cap is at a relatively low level. However, the carbon price may not remarkably affect the manufacturer’s cost because its influence could be abated through the flexible technology switch under the emission cap-and-trade scheme.