Cost-Duration Analysis with the Cut Network

A new approach is developed for conducting a cost-duration analysis (trade-off study) for a project denned with a CPM/PERT activity network. The approach utilizes a new graph theory concept, proper oriented cut-set (POCS). It also uses the cut network, a dual-type network defined in this paper for any planar activity network. The cut network implicitly enumerates all POCS's of an original network. The cost-duration problem defined for the original activity network is transformed into a minimum-cost flow problem for the cut network. This approach to cost-duration analysis, developed here for a planar network and linear activity cost-duration relations, is optimal, conceptually direct, and has potential for application to more general cost-functions.