Successive approximations procedures for a cellular manufacturing problem with machine loading constraints

The task of partitioning a collection of machines into autonomous production centers is well-known and the arrangement is denoted ‘cellular manufacturing’. The problem itself is one of discrete optimization, and a successive approximations method which has proven a good solution technique is reviewed. Individual machine loading constraints are then introduced and a variety of mathematical formulation alternatives, including quadratic integer programming and set covering, pursued for that more realistic and considerably more complicated problem. Solution procedures for the various formulations are discussed.