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

TL;DR

This paper develops robust optimization models for routing and scheduling multi-skilled teams under uncertain job skill requirements, ensuring solutions remain effective despite data variations.

Contribution

It introduces two novel robust modeling approaches using budgeted uncertainty for team routing and scheduling under uncertain qualifications.

Findings

Both approaches effectively handle data uncertainty.

The first approach is computationally efficient with little added complexity.

The second approach offers a more comprehensive robustness at manageable complexity.

Abstract

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.