Solving a real-world train-unit assignment problem

Cacchiani, Valentina; Caprara, Alberto; Toth, Paolo

doi:10.1007/s10107-010-0361-y

Cited by 79 publications

(100 citation statements)

References 23 publications

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“…Bodin et al (1983) give a general survey on vehicle scheduling. Maróti (2006) and Cacchiani et al (2010) have reviewed relevant railway scheduling problems. Researches specifically on train unit scheduling are relatively few.…”

Section: Literature Reviewmentioning

confidence: 99%

“…More recently, Cacchiani et al (2010) propose an integer MCNF model solved by column generation with shortest path subproblems including some heuristic methods to improve efficiency. This model takes considerations of coupling/decoupling and vehicle-route compatibility, and is reported to have been applied for real-world instances of up to 600 train trips.…”

Section: Train Sequencing and Fleet Assignment Problemmentioning

confidence: 99%

“…The first phase for train sequencing and fleet assignment uses an MCNF model similar to Cacchiani et al (2010). But the model is more comprehensive in modeling real-world conditions and constraints typical of railway operations, especially the coupling/decoupling time allowance constraints and type compatibility constraints.…”

Section: A Multi-commodity Flow Model For the First Phasementioning

confidence: 99%

“…The LP-relaxations of the two formulations are equivalent (Cook et al (1998);Cacchiani et al (2010)). We choose an LP-relaxation rather than a Lagrangian relaxation as nowadays a state-of-art simplex solver can be more efficient than a subgradient method.…”

Section: Path Formulationmentioning

confidence: 99%

“…The first phase is mainly a train sequencing and fleet assignment problem, leaving the resolution of how the train units would feasibly flow through the precise station layouts to the second phase. An integer multi-commodity network flow (MCNF) model similar to Cacchiani et al (2010), but more comprehensive in modeling the real-world conditions and constraints typical of UK rail operations, is used in the first phase. Fleet size and type constraints, linkage time allowance validity and coupling/decoupling possibilities are included in the model.…”

Section: Introductionmentioning

confidence: 99%

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A two-phase approach for real-world train unit scheduling

Lin

Kwan

2013

Public Transp

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A two-phase approach for the train unit scheduling problem is proposed. The first phase assigns and sequences train trips to train units temporarily ignoring some infrastructure details at train stations. The solutions of the first phase would be near-operable. The second phase focuses on satisfying the remaining constraints with respect to detailed station layouts. Real-world scenarios such as compatibility among traction types and time allowances for coupling/decoupling activities are considered, so that the solutions would be fully operable.The first phase is modeled as a large scale integer multi-commodity network flow (MCNF) problem. A branch-and-price integer linear programming approach is proposed. Preliminary experiments have shown that the approach would not yield solutions in reasonable time for problem instances exceeding about 1000 train trips. The train company collaborating in this research operates over 2400 train trips on a typical weekday. Hence, a heuristic has been designed for compacting the problem instance to a much smaller size before the ILP solver is applied. The process is iterative with evolving compaction based on the results from the previous iteration thereby converging to near optimal results.The second phase is modeled as a multidimensional matching problem with a mixed integer linear programming (MILP) formulation.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Train Sequencing and Fleet Assignment Problemmentioning

confidence: 99%

Section: A Multi-commodity Flow Model For the First Phasementioning

confidence: 99%

Section: Path Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A two-phase approach for real-world train unit scheduling

Lin

Kwan

2013

Public Transp

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Optimization Problems in Passenger Railway Systems

Caprara

Kroon

Toth

2011

Wiley Encyclopedia of Operations Research and Management Science

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This article describes the main optimization problems that are faced in the planning of a passenger railway system, from the definition of the routes and frequencies of the trains in the railway network to the construction of the duties and the rosters for drivers and conductors. These problems are presented in the order in which they are faced in practice, illustrating what they are aimed at, and how they are solved by mathematical programming techniques. The article also briefly illustrates recent advances in producing “robust” (i.e., fault‐tolerant) solutions for these problems, and in the application of optimization methods for real‐time recovery of railway systems.

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A learning tabu search for a truck allocation problem with linear and nonlinear cost components

Schindl¹,

Zufferey

2014

Naval Research Logistics

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The two-level problem studied in this article consists of optimizing the refueling costs of a fleet of locomotives over a railway network. The goal consists of determining: (1) the number of refueling trucks contracted for each yard (truck assignment problem denoted TAP) and (2) the refueling plan of each locomotive (fuel distribution problem denoted FDP). As the FDP can be solved efficiently with existing methods, the focus is put on the TAP only. In a first version of the problem (denoted (P1)), various linear costs (e.g., fuel, fixed cost associated with each refueling, weekly operating costs of trucks) have to be minimized while satisfying a set of constraints (e.g., limited capacities of the locomotives and the trucks). In contrast with the existing literature on this problem, two types of nonlinear cost components will also be considered, based on the following ideas: (1) if several trucks from the same fuel supplier are contracted for the same yard, the supplier is likely to propose discounted prices for that yard (Problem (P2)); (2) if a train stops too often on its route, a penalty is incurred, which represents the dissatisfaction of the clients (Problem (P3)). Even if exact methods based on a mixed integer linear program formulation are available for (P1), they are not appropriate anymore to tackle (P2) and (P3). Various methods are proposed for the TAP: a descent local search, a tabu search, and a learning tabu search (LTS). The latter is a new type of local search algorithm. It involves a learning process relying on a trail system, and it can be applied to any combinatorial optimization problem. Results are reported and discussed for a large set of instances (for (P1), (P2), and (P3)), and show the good performance of LTS

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Solving a real-world train-unit assignment problem

Cited by 79 publications

References 23 publications

A two-phase approach for real-world train unit scheduling

A two-phase approach for real-world train unit scheduling

Optimization Problems in Passenger Railway Systems

A learning tabu search for a truck allocation problem with linear and nonlinear cost components

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