Equitable Routing--Rethinking the Multiple Traveling Salesman Problem
For researchers and practitioners in routing optimization, this work provides a practical and flexible alternative to the min-max MTSP by introducing fairness constraints with global optimality guarantees.
This paper introduces two new fairness-driven variants of the Multiple Traveling Salesman Problem (MTSP) that promote equitable distribution of tour lengths while controlling overall cost, and develops algorithms guaranteeing global optimality. Experiments on benchmark instances and real-world electric vehicle fleet routing demonstrate their effectiveness, and the algorithms can obtain the Pareto front of a bi-objective optimization problem.
The Multiple Traveling Salesman Problem (MTSP) extends the traveling salesman problem by assigning multiple salesmen to visit a set of targets from a common depot, with each target visited exactly once while minimizing total tour length. A common variant, the min-max MTSP, focuses on workload balance by minimizing the longest tour, but it is difficult to solve optimally due to weak linear relaxation bounds. This paper introduces two new parametric fairness-driven variants of the MTSP: the $\varepsilon$-Fair-MTSP and the $Δ$-Fair-MTSP, which promote equitable distribution of tour lengths while controlling overall cost. The $\varepsilon$-Fair-MTSP is formulated as a mixed-integer second-order cone program, while the $Δ$-Fair-MTSP is modeled as a mixed-integer linear program. We develop algorithms that guarantee global optimality for both formulations. Computational experiments on benchmark instances and real-world applications, including electric vehicle fleet routing, demonstrate their effectiveness. Furthermore, we show that the algorithms presented for the fairness-constrained MTSP variants can be used to obtain the Pareto front of a bi-objective optimization problem in which one objective minimizes the total tour length and the other balances the lengths of the individual tours. Overall, these fairness-constrained MTSP variants provide a practical and flexible alternative to the min-max MTSP.