On the computational complexity of the minimum‐dummy‐activities problem in a pert network

Abstract

AbstractThe scheduling and planning of a project can be represented by two types of networks, namely, by the activity networks and the event networks. For each project, there exists a unique activity network without redundant (transitive) arcs but since there is an infinite number of different‐sized event networks, the problem is to find an event network with the minimum number of dummy activities. Krishnamoorthy and Deo proved that this problem is NP‐complete. In Sections III and IV we characterize those activity networks which have event networks without dummy activities and present a polynomial‐time algorithm which tests if a given activity network requires dummy activities in the event network. The same result is also proved for a generalization of the real‐world problem to arbitrary digraphs. Finally, we present an example which shows that the number of nodes and the number of arcs in event networks cannot be minimized simultaneously.