COST TIME TRADE-OFF ANALYSIS FOR THE CRITICAL PATH METHOD - A DERIVATION OF THE NETWORK FLOW APPROACH/

A well-known problem in critical path analysis involves normal and cra sh durations being provided for each activity, with. corresponding cos ts, and requires a minimum cost schedule of durations to be determined for all possible durations of the project. It has long been known tha t an optimal solution to the problem can be obtained iteratively by co nstructing a minimum cost network flow problem and adjusting the durat ions of activities corresponding to a minimum capacity cut-set. A rece nt paper described this method, but gave no indication of how the meth od could be derived. It is shown here that a linear programming formul ation and its dual enables this to be done very simply.