Cash Flows in Networks

The concept of maximising present value is applied to the timing of activities in a network. The mathematical form of the problem is that of maximising a nonlinear function subject to linear constraints and can be solved as a succession of linear programmes. By application of duality principles the problem can be treated as a form of maximum value flow problem in which discounted cash flows are distributed along arcs from pay events to receipt events. The solution is aided by the "equilibrium theorem" of dual linear programming in that in the optimum condition flows occur only along arcs whose corresponding activity has zero float. The flows which occur in the optimally scheduled solution are directly proportional to the marginal cost which would be incurred by lengthening the activity corresponding to the arc along which the flow occurs. Some implications derived from the model are discussed and a number of possible applications are proposed.