Efficient solving of the group technology problem

In this paper, two formulations of the group technology problem are considered: the standard formulation and the augmented formulation. The standard formulation is based on the 0-1 machine-incidence matrix and does not consider any costs. In the augmented formulation with each part j, cost c//j is associated and the number of machines in each cell is limited to N. This formulation allows the creation of machine cells and part families with a low degree of interaction (or without any interaction, if required) by removing parts with low values of the corresponding costs from the incidence matrix. To solve these formulations, two very efficient algorithms are presented.