Block angular structures and the loading problem in Flexible Manufacturing Systems

Loading problems of Flexible Manufacturing Systems (FMSs) have usually been formulated as an integer program with nonlinear constraints for tool magazine capacities. The nonlinearity and integer nature of the problem results in the loading problem being difficult to solve. Conventional branch-and-bound methods have been proposed, but again the solution time can easily be excessive for moderate sized problems. In this paper, the authors present an alternative formulation of the FMS loading problem. Such a formulation defines more decision variables, but is able to avoid nonlinearity of the constraints. It also includes the time availabilities of the machines as additional constraints. The main feature of the formulation is that it exhibits a block angular structure. By exploiting this special structure, an efficient branch-and-bound algorithm can be developed. This algorithm has the attractive feature that the bounds of the branches can be computed through simple procedures based on the solution of linear knapsack problems. Some computational results of the algorithm are also presented.