Optimal Time-Cost Trade-Offs in GERT Networks

Abstract

Optimal time-cost trade-offs in deterministic networks of the CPM-type have been neatly resolved by Fulkerson. In the case of GERT-type networks, the problem is complicated by the randomness in the duration of the activity and in the likelihood of its existence. Assuming linear relationships between additional investments and expected duration and additional cost, a model is formulated in which we seek the maximization of the marginal reduction in duration per unit of investment. This, in turn, leads to a fractional linear program whose solution is obtained easily.