A Branch-and-Price algorithm for stable workforce assignments with hierarchical skills

“…Following these initial contributions, an increasing number of extensions has been presented. For instance, such features as routing of teams (Kovacs et al, 2012), multi-period planning (Zamorano and Stolletz, 2017), employee preferences for performing a specific job (Fırat et al, 2016), alternative heuristic solution methods (Khalfay et al, 2017), decomposition techniques (Anoshkina and Meisel, 2019) as well as team consistency and rescheduling (Anoshkina and Meisel, 2020) have been studied. A more detailed description of these studies is provided by Anoshkina and Meisel (2020).…”

Section: Literaturementioning

confidence: 99%

Robust Optimization Approaches for Routing and Scheduling of Multi-Skilled Teams under Uncertain Job Skill Requirements

Anoshkina¹,

Goerigk²,

Meisel³

2020

Preprint

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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 are 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.

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“…A common feature of these papers that the laminar nature of the set requirements makes the problem polynomial time solvable. A closely related model was studied in [22] without the laminar assumption, where the problem was proved to by NP-hard and was solved by integer programming techniques.…”

Section: Within-type Prioritiesmentioning

confidence: 99%

Stable project allocation under distributional constraints

Ágoston

Bíró

Szántó

2018

Operations Research Perspectives

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In a two-sided matching market when agents on both sides have preferences the stability of the solution is typically the most important requirement. However, we may also face some distributional constraints with regard to the minimum number of assignees or the distribution of the assignees according to their types. These two requirements can be challenging to reconcile in practice. In this paper we describe two real applications, a project allocation problem and a workshop assignment problem, both involving some distributional constraints. We used integer programming techniques to find reasonably good solutions with regard to the stability and the distributional constraints. Our approach can be useful in a variety of different applications, such as resident allocation with lower quotas, controlled school choice or college admissions with affirmative action.

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A Branch-and-Price algorithm for stable workforce assignments with hierarchical skills

Cited by 17 publications

References 25 publications

Column generation based heuristic for learning classification trees

Column generation based heuristic for learning classification trees

Robust Optimization Approaches for Routing and Scheduling of Multi-Skilled Teams under Uncertain Job Skill Requirements

Stable project allocation under distributional constraints

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