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arXiv · 2607.10459

A column generation-based fixed-point heuristic for the service-aware multi-commodity flow problem

Siv Marie Cartland Hansen·Richard Martin Lusby
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Abstract

We study the Service-Aware Multi-Commodity Flow (SAMCF) problem, in which demand is elastic and governed by a logit choice model while routing is subject to hard capacity constraints. In a centralized, system-optimal setting, the network operator jointly determines how much demand to serve and how to route it. We formulate the SAMCF as a nonlinear program and propose an iterative fixed-point heuristic that alternates between solving an inelastic MCF via column generation and updating demand from the resulting service levels. Two linear approximations based on piecewise-linear demand functions and McCormick envelopes serve as benchmarks, while a piecewise-linear outer-approximation of the demand function is used to provide valid lower bounds. Computational experiments on public transport instances show that the heuristic finds near-optimal solutions in under two seconds - orders of magnitude faster than the benchmark methods - while matching their solution quality on all instances they can solve within a ten-minute time limit.

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Siv Marie Cartland Hansen, Richard Martin Lusby. 2026-07-11. A column generation-based fixed-point heuristic for the service-aware multi-commodity flow problem. https://arxiv.org/abs/2607.10459

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