Abstract: Resource constraints are often broadly impacting, unavoidable impediments in project execution procedures. A number of recent, topical project management issues, such as the resource-constrainedproject scheduling problem (RCPSP), have their roots in the resource constraint problem. It is NP-hard in the strong sense. Current research on the RCPSP mainly focuses on the global problemin which all activities are constrained by resource constraints during the whole project process. Considering practical projects requiring numerous types of resources, the “resource constrained” designation may be for limited types of resources or during local project processes. The local “resource-constrained” designation may constrain activities in a part of the projectsuch that only a portion of activities need arrangement under resource restriction.The above representation denotes the local RCPSP.In this paper, a typical sub-problem of the local RCPSP is studied, which is generated by adding some special assumptions to the general local RCPSP.

Key words: resource-constrained project scheduling; strong duality of integer programming; exact polynomial time algorithm; Dangzig-Wolfe decomposition