Resource overload problems with tardiness penalty: structural properties and solution approaches

In this paper, we consider a resource overload problem and add a tardiness penalty to the objective function when a prescribed project makespan is exceeded, which enables a trade-off between a balanced resource utilization and a project delay. For the tardiness penalty, we distinguish between a constant and variable delay cost variant. Based on the structural properties of the resource overload problem, we show that the search space of the resource overload problem with tardiness penalty can also be reduced utilizing quasistable schedules. In addition, we discuss the application of these findings to further problems, which include objectives composed of a locally concave and a concave function or a reward structure for an early project completion instead of a tardiness penalty. As solution approaches, we present mixed-integer linear model formulations as well as a novel genetic algorithm with a decoding procedure, which exploits the devised structural properties. The performance of the genetic algorithm is improved by implementing learning methods and utilizing lower bounds. Finally, we present results from experiments on small to medium sized problem instances.