A new path-based cutting plane approach for the discrete time-cost tradeoff problem

Determining discrete time-cost tradeoffs in project networks allows for the control of the processing time of an activity via the amount of non-renewable resources allocated to it. Larger resource allocations with associated higher costs reduce activities' durations. Given a set of execution modes (time-cost pairs) for each activity, the discrete time-cost tradeoff problem (DTCTP) involves selecting a mode for each activity so that either: (i) the project completion time is minimized, given a budget, or (ii) the total project cost is minimized, given a deadline, or (iii) the complete and efficient project cost curve is constructed over all feasible project durations. The DTCTP is a problem with great applicability prospects but at the same time a strongly NP-hard optimization problem; solving it exactly has been a real challenge. Known optimal solution methodologies are limited to networks with no more than 50 activities and only lower bounds can be computed for larger, realistically sized, project instances. In this paper, we study a path-based approach to the DTCTP, in which a new path-based formulation in activity-on-node project networks is presented. This formulation is subsequently solved using an exact cutting plane algorithm enhanced with speed-up techniques. Extensive computational results reported for almost 5,000 benchmark test problems demonstrate the effectiveness of the proposed algorithm in solving to optimality for the first time some of the hardest and largest instances in the literature. The promising results suggest that the algorithms may be embedded into project management software and, hence, become a useful tool for practitioners in the future.