An efficient heuristic approach to recognize the infeasibility of a loading problem

The success of hierarchical production planning approaches for flexible manufacturing systems lies in the consistency of decision outcomes at various decision levels. For instance, the loading problem, which is solved at a lower level, may not yield a feasible loading solution to a set of part types selected at a higher level. This paper attempts to address the issue of recognizing the infeasibility of a loading solution. We present a modified loading model that includes a penalty for each operation not assigned to any machine. We develop a Lagrangian-based heuristic procedure and provide a sufficient condition on the quality of heuristic solutions that, if satisfied, will enable us to use the heuristic solutions to recognize the infeasibility of a loading problem. The proposed model and the dual-based heuristic can be effectively incorporated in an FMS hierarchical production planning approach that finds a good loading solution by iteratively comparing different part grouping scenarios.