We consider a combined problem of teaming and scheduling of multi-skilled employees that have to perform jobs with uncertain qualification requirements. We propose two modeling approaches that generate solutions that are robust to possible data variations. Both approaches use variants of budgeted uncertainty, where deviations in qualification requirements are bounded by a constraint. In the first approach, we aggregate uncertain constraints to ensure that the total number of job qualifications present at a job is not less than a worst-case value. We show that these values can be computed beforehand, resulting in a robust model with little additional complexity compared with the nominal model. In our second approach, we bound the overall qualification deviation over all jobs. While this approach is more complex, we show that it is still possible to derive a compact problem formulation by using a linear programming formulation for the adversarial problem based on a dynamic program. The performance of both approaches is analyzed on a test bed of instances which were originally provided for a deterministic problem version. Our experiments show the effectiveness of the proposed approaches in the presence of data uncertainty and reveal the price and gain of robustness.
Dynamic Core Allocation for Malleable Jobs with Unknown Speed-up Parameters
Korteweg-de Vries Institute for Mathematics, University of Amsterdam（阿姆斯特丹大学科特维格-德弗里斯数学研究所）；Mathematical Institute, Leiden University（莱顿大学数学研究所）；Eurandom, Eindhoven University of Technology（埃因霍温理工大学尤拉当）；Department of Statistics, University of Haifa（海法大学统计学系）
