A Structural Method of Computing Project Cost Polygons - Prager, William (Management Science, 1963)
For a project that consists of numerous jobs subject to technological ordering restrictions the polygon representing project cost versus completion time is to be determined when the normal and crash completion times are known for each job and the cost of doing the job varies linearly between these times. A linear programming formulation of this problem was given by Kelley [Kelley, J. E., Jr. 1961. Critical-path planning and scheduling: Mathematical basis. Oper. Res. 9 296–320.] and a network flow formulation by Fulkerson [Fulkerson, D. R. 1961. A network flow computation for project cost curves. Management Sci. 7 (2, January) 167–178.]. Since the traditional mathematical background of civil engineers includes neither linear programming nor network flow theory, these methods are not as widely used in the building industry as they deserve. This paper shows that Fulkerson's algorithm can be given a structural interpretation using concepts that are familiar to civil engineers.