Stochastic Lot Sizing Problem with Carbon Emission Constraints

Abstract

In this paper, we study the stochastic lot sizing problem with probabilistic carbon emission constraints under the static uncertainty strategy and α service level constraints. We consider both the periodic and global carbon emission constraints and guarantee that the carbon emission constraints are met with the desired probabilities by using chance constraints. Though this problem can be observed in many real life production systems today, to the best of our knowledge, this is the first study on this problem. We formulate the problems as mixed integer linear programs and solve them by a commercial solver. In our computational experiments, we observe 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 under different parameter settings, and present insights about the consequences of using these restrictions.