Nowadays, with the increase of global temperature due to human activities, attention to environmental issues such as controlling the emission of greenhouse gases such as carbon dioxide and also the management of energy consumption (electricity) in manufacturing organizations is one of the particular importance. Therefore, in order to control the amount of carbon dioxide emissions and create a balance of energy consumption between peak and off-peak hours, in this study we introduce the problem of green capacitated multi-item lot sizing problem on parallel machines with backlog by considering the critical energy-peak times. In this case, despite the two assumptions of buying a new machine and lost sale in each period, it is possible for the model, depending on the cost of lost sale or the cost of buying a new machine to choose one of these two modes in each period. For this problem a mixed integer programming model is proposed. In the fallowing we obtain a lower bound for the problem by Dantzig-Wolfe algorithm.
