Problem
Research questions and friction points this paper is trying to address.
technician routing and scheduling
lexicographic optimization
electricity distribution
multi-objective optimization
workforce scheduling
A column-generation approach for an electricity technician routing and scheduling problem with a lexicographic objective
🤖 AI Summary
This study addresses the technician dispatching problem faced by electric utilities, which involves scheduling a large number of intervention tasks within a limited time horizon, with the primary objective of maximizing the total duration of completed tasks and the secondary objective of minimizing operational costs. The work introduces lexicographic multi-objective optimization to this domain for the first time and proposes a sequential column generation algorithm that transforms the multi-objective problem into a sequence of single-objective problems via weighted summation and hierarchical optimization. The approach integrates an extended set-covering formulation, mixed-integer linear programming, and a dynamic programming–based labeling algorithm to solve the pricing subproblem. Experiments on real-world data from Électricité de France demonstrate that the method yields superior solutions on small instances and produces high-quality schedules within five minutes for large-scale instances, achieving lower average optimality gaps and improving upon several best-known solutions.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
column generation
lexicographic optimization
technician routing and scheduling
dynamic programming labeling
multi-objective combinatorial optimization
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