Recent advances in mathematical programming for cell formation

Cell formation, one major problem with cellular manufacturing, involves the process of grouping the parts with similar design features or processing requirements into part families and the corresponding machines into machine cells. Numerous analytical approaches to solve the problem have been introduced, among which mathematical programming models and heuristic procedures constitute the greatest part of the literature. This chapter presents a state-of- the-art review based on a systematic survey of the literature. Survey results should help answer or clarify many related questions for the cellular manufacturing community. Examples have been provided to help the interested reader use earlier studies to develop mathematical programming models. The purpose of this study is twofold: (1) to examine the state-of-the-art of mathematical programming's use in cell formation and (2) to illustrate the way by which a variety of cell formation problems can be formulated by means of mathematical programming. Examples with different objectives, constraints, and structures are provided, which not only represent typical cell formation problems, but also can be used to demonstrate the way by which the same scenario can be modeled through either objectives or constraints.