A column-generation approach for an electricity technician routing and scheduling problem with a lexicographic objective
This work addresses operational efficiency for electric utility companies by optimizing daily technician schedules, though it is incremental as it builds on existing routing and scheduling methods with a specific lexicographic twist.
The paper tackled the technician routing and scheduling problem for electric utility companies by introducing a lexicographic multi-objective approach to maximize completed intervention duration and minimize costs, with a column-generation algorithm that outperformed a compact formulation in computational experiments, achieving lower mean gaps and better solutions on real-life instances.
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.