Solving a new robust green cellular manufacturing problem with environmental issues under uncertainty using Benders decomposition

A cellular manufacturing system is a practical tool of group technology philosophy in a production environment. Although environmental issues have a significant impact on production processes, green considerations have not been studied in detail for such problems. This article aims to fill the gap by proposing a new mathematical model in which environmental issues, such as pollution caused by production and transportation modes, as well as waste, are considered. In addition, production planning and inventory balance among different periods are considered. Moreover, it is assumed that the processing times of products are uncertain and so a robust optimization approach is used to handle such uncertainty. The presented model is solved by the Benders decomposition algorithm. According to the outputs, the demand has the greatest effect on cell formation cost. Finally, the effect of green parameters on optimality is investigated.