Solution space analysis of manufacturing scheduling problems

This paper proposes a new method of analyzing the solution space of multi-factor manufacturing scheduling problems. The proposed method is introduced together with two new concepts: relation matrix and decision matrix. This method simplifies a multi-factor problem into a number of two-factor sub-problems which are then analyzed individually. Some close-expressions of the number of feasible solutions for multi-device, multi-worker and multi-task are obtained. It can be used not only to calculate the number of possible/feasible solutions, but also to obtain these solutions in simple cases. It is particularly useful in very complex situations, since the results of solution space analysis can help choose appropriate techniques or algorithms to solve complex scheduling problems.