The green capacitated multi-item lot sizing problem with parallel machines

•We propose a mixed integer programming model for the green capacitated multi-item lot sizing problem with parallel machines.•The mathematical model can support the reduction of carbon emissions for manufacturing companies.•The green lot sizing problem is NP-hard and is therefore difficult to solve.•We apply a progressive selection heuristic to find feasible solutions and upper bounds for the problem.•We also apply Lagrangian-relaxation, Dantzig–Wolfe decomposition, and column generation to enhance lower bounds for quantifying the solution quality.