A column-generation approach for an electricity technician routing and scheduling problem with a lexicographic objective

TL;DR

This paper introduces a novel column-generation approach for a multi-objective technician routing problem with lexicographic priorities, demonstrating improved solution quality and computational efficiency on real utility data.

Contribution

It develops a new exact column-generation algorithm with labeling-based pricing for a lexicographic multi-objective routing problem, outperforming traditional formulations.

Findings

The CG-based algorithm finds optimal solutions on more small instances than the compact formulation.

It outperforms the compact formulation on larger instances in solution quality.

Sequential reformulations achieve the best-known solutions with lower gaps.

Abstract

Electric utility companies perform numerous technical interventions every day. Since it is generally not possible to complete all planned interventions within a single day, companies face two objectives: maximizing the total duration of completed interventions (primary objective) and minimizing the associated operational cost (secondary objective). In this paper, we introduce a multi-objective variant of the technician routing and scheduling problem in which both objectives are optimized in lexicographic order. We propose a compact mixed-integer linear formulation and an extended set-packing-based formulation. To handle the objectives within a single-objective framework, we consider weighted-sum reformulations that preserve lexicographic priorities as well as sequential reformulations that individually optimize each objective while maintaining the optimal value of higher-priority ones. For the extended formulation, we develop an exact column-generation-based algorithm, in which the pricing subproblems are solved via a labeling algorithm based on dynamic programming. As technician schedules are typically generated on a daily basis, the algorithm is designed to deliver high-quality solutions within short computation times (e.g., 5 minutes). Computational experiments on real-life instances provided by the French electric utility company show that the CG-based algorithm proves optimality on a larger number of small instances than the compact formulation and consistently outperforms it on larger instances. In particular, the sequential CG-based variant finds the best-known solutions on more instances and achieves lower mean gaps relative to the best solution found in each instance category.