A robust optimisation approach to project scheduling and resource allocation

In a rapidly changing and highly uncertain environment, Petri net-based project management systems can be used in the rescheduling (control reconfiguration) of projects, when unforeseen changes occur or new data estimates become available. However, having to reschedule the project after it has started can result in significant suboptimality due to increased cost. In this paper, we present a solution method which is, to a large extent, robust to data uncertainty and does not require rescheduling for a certain predefined level of uncertainty. We build the model using robust optimisation techniques which address data uncertainty in project parameters, by taking advantage of risk pooling and without knowledge of their probability distributions. We illustrate that the total cost when the robust solution is used is generally lower than the cost of reconfiguring the deterministic solution, or than a penalty cost due to overtime of the deterministic solution, for a high enough penalty cost per time unit. We find that the robust solution is better protected against constraint violations, including time and cost overruns.