A complete complexity study of one-processor assembly and manufacturing planning tasks

This paper deals with a method to compute the number of plans that exist for an assembly or processing task. Since planning is a NP-hard problem, the application of some search methods must be avoided. However, up to now, the computation of the exact number of alternative plans for complex tasks and considering precedence constraints has not been performed. It is shown that the complexity of the problem does not depend just on the number of involved operations, components or parts. The complexity of the problem depends on the topology of the precedence between operations.