Lot sizing with carbon emission constraints

This paper introduces new environmental constraints, namely carbon emission constraints, in multi-sourcing lot-sizing problems. These constraints aim at limiting the carbon emission per unit of product supplied with different modes. A mode corresponds to the combination of a production facility and a transportation mode and is characterized by its economical costs and its unitary carbon emission. Four types of constraints are proposed and analyzed in the single-item uncapacitated lot-sizing problem. The periodic case is shown to be polynomially solvable, while the cumulative, global and rolling cases are NP-hard. Perspectives to extend this work are discussed.

► We introduce four new environmental constraints in lot-sizing problems.
► Mathematical programming models for the single-item lot-sizing problem are introduced.
► A polynomial dynamic program is proposed for the periodic carbon emission constraint.
► It is shown that the problem is NP-hard with any of the three other constraints.