The theory of networks and management science. Part I

An expository treatment of three network models most often encountered in Management Science applications: (i) The Shortest Path Problems, (ii) Flow Networks, and (iii) Activity Networks. In the first problem are discussed the shortest path between two specified nodes; the shortest distance matrix; as well as the special case of directed acyclic networks. In the second problem, a brief exposition of the "labeling procedure" leads into multiterminal networks and the general minimal cost circulation problem and a discussion of the "out-of-kilter" method. In the third problem, the "classical" models of CPM and PERT are reviewed, together with a discussion of generalized activity networks and the viewing of GERT as a signal flow graph of a semi-Markov process. Illustrations of the application of each model are also given. The first two models appear in the September issue; and the third model in the October issue of Management Science.