Minimization of the Worst-Case Makespan

Abstract

In this chapter we study a robust resource allocation problem that minimizes the worst-case makespan. As in the previous chapters, we assume that the resource allocation is a here-and-now decision, whereas the task start times are modeled as a wait-and-see decision that may depend on random parameters affecting the task durations. In the terminology of Sect. 2.2.2, we therefore study a two-stage robust optimization problem. In contrast to its stochastic counterpart, the complexity of the robust resource allocation problem has been unknown for a long time [Hag88]. The majority of the solution approaches presented in the literature determine suboptimal solutions without bounding the incurred optimality gap.