arXiv subjects

Rolf van Lieshout

Publications and source records attributed to Rolf van Lieshout.

4 recordsLinked to original sources

arXiv2026

Line Planning at Scale: Models, Methods, and Insights

Line planning, the problem of deciding which lines to operate and at what frequency, is a fundamental step in public transport planning. To accurately model passenger routing, the problem is traditionally defined on a change-and-go network (CGN), which captures transfers between lines exactly. However, this network grows large quickly and is hard to solve at scale. We compare the CGN against three more compact models, differing with respect to how transfers are approximated, and characterize how they relate in terms of solution quality and modeling accuracy. We develop state-of-the-art solution methods tailored to each model, and evaluate all four across 972 instances based on the Dutch and Swiss railway networks. Contrary to the CGN's canonical status, we find that it is competitive only on small or easy instances and often fails to find any feasible solution on large networks. Instead, a compact direct connection model performs best overall, finding the best solution on over 83% of instances. Our results indicate that carefully designed approximations, rather than exact transfer modeling, are the more promising foundation for large-scale line planning.

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arXiv2026

Adaptive Partitioning in Column Generation for Nested Paths

We study a class of nested path problems, in which every path-based variable can be decomposed into a sequence of subpaths. Subpaths must satisfy local resources, while paths must satisfy additional global resources. This paper develops a new exact pricing algorithm in column generation for these problems that avoids the enumeration of non-dominated subpaths. The algorithm relies on adaptive partitioning of subpaths into buckets characterizing the consumption of global path resources. The algorithm represents each bucket by its subpath of minimum reduced cost, and iterates between pessimistic and optimistic pricing steps to combine subpaths into paths while maintaining upper and lower bounds on the minimum reduced cost. An adaptive refinement procedure closes the gap in a finite number of iterations. We demonstrate the effectiveness of the algorithm on two applications. For the balanced multi-period capacitated vehicle routing problem, we obtain speed-ups of up to a factor of 13 over a state-of-the-art column generation benchmark, and the resulting branch-price-and-cut algorithm solves three times as many instances to optimality as a subpath-based baseline. For the robust railway crew scheduling problem, we obtain speed-ups of up to a factor of three and produce primal solutions within 1% of optimality.

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arXiv2025

The Fair Periodic Assignment Problem

We study the periodic assignment problem, in which a set of periodically repeating tasks must be assigned to workers within a repeating schedule. The classical efficiency objective is to minimize the number of workers required to operate the schedule. We propose a O(n log n) algorithm to solve this problem. Next, we formalize a notion of fairness among workers, and impose that each worker performs the same work over time. We analyze the resulting trade-off between efficiency and fairness, showing that the price of fairness is at most one extra worker, and that such a fair solution can always be found using the Nearest Neighbor heuristic. We characterize all instances that admit a solution that is both fair and efficient, and use this result to develop a O(n log n) exact algorithm for the fair periodic assignment problem. Finally, we show that allowing aperiodic schedules never reduces the price of fairness.

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arXiv2023

Dynamic Discretization Discovery for the Multi-Depot Vehicle Scheduling Problem with Trip Shifting

The solution of the Multi-Depot Vehicle Scheduling Problem (MDVSP) can often be improved substantially by incorporating Trip Shifting (TS) as a model feature. By allowing departure times to deviate a few minutes from the original timetable, new combinations of trips may be carried out by the same vehicle, thus leading to more efficient scheduling. However, explicit modeling of each potential trip shift quickly causes the problem to get prohibitively large for current solvers, such that researchers and practitioners were obligated to resort to heuristic methods to solve large instances. In this paper, we develop a Dynamic Discretization Discovery algorithm that guarantees an optimal continuous-time solution to the MDVSP-TS without explicit consideration of all trip shifts. It does so by iteratively solving and refining the problem on a partially time-expanded network until the solution can be converted to a feasible vehicle schedule on the fully time-expanded network. Computational results demonstrate that this algorithm outperforms the explicit modeling approach by a wide margin and is able to solve the MDVSP-TS even when many departure time deviations are considered.

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