Two topics in the part-machine cell formation problem are discussed: In the first part, a Lagrangean relaxation in a mathematical programming model is proposed to simultaneously set machines into groups and parts into families in a cellular manufacturing system. The objective of this model is to find the optimal number of cells while minimizing inter-cellular part moves and increasing utilization of machines within the cells. The method uses a 0-1 integer programming model. The Lagrangean relaxation relaxes the model through an iterative search. In the second part, we introduce a new performance measure and compare it to some known performance measures. The new measure preserved some important features of previous performance measures and overcomes a number of drawbacks. Both the measure and the model are applied to benchmark problems as well as randomly generated problems. The new measure and model are comparable to the existing models and measures
