Stochastic Lot Sizing Problem with Carbon Emission Constraints

In this paper, we study the stochastic lot sizing problem with probabilistic carbon emission constraints. To the best of our knowledge, this is the first study that considers this problem. We study the problem under static uncertainty strategy and α service level constraints. We consider both the periodic and global carbon emission constraints and use chance constraints to ensure that the carbon emission constraints are satisfied with the desired probabilities. We formulate the problems as mixed integer program and solve them by a commercial solver. Our computational experiments show that the formulations can be solved for quite large problem instances in reasonable times. We compare the probabilistic global and periodic emission constraints according to their effects on the total cost and carbon emissions.