Combining Benders decomposition and column generation for multi-activity tour scheduling

Restrepo, María Isabel; Gendron, Bernard; Rousseau, Louis-Martin

doi:10.1016/j.cor.2018.01.014

Cited by 16 publications

(10 citation statements)

References 36 publications

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“…(1) In our case studies, with the Benders cuts added to BMP, the model becomes more and more difficult to handle by optimization software. An efficient algorithm should be further developed to solve BMP, such as the three-phase method [24,25], which has one more phase because it relaxes all integrality constraints in the BMP in first phase and reintroduces the integrality constraints to the BMP in the next phase.…”

Section: Discussionmentioning

confidence: 99%

“…The approach that combines Benders decomposition and column generation has been applied to other simultaneous problems in transportation, such as locomotives and cars assignment to passenger trains problem [22], and aircraft routing and crew scheduling problem [23]. For more recent literature about this approach, we refer the reader to Restrepo et al [24].…”

Section: Solution Methodsmentioning

confidence: 99%

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Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach

Lan

Song

et al. 2019

Journal of Advanced Transportation

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In practice, vehicle scheduling is planned on a variable timetable so that the departure times of trips can be shifted in tolerable ranges, rather than on a fixed timetable, to decrease the required fleet size. This paper investigates the vehicle scheduling problem on a variable timetable with the constraint that each vehicle can perform limited trips. Since the connection-based model is difficult to solve by optimization software for a medium-scale or large-scale instance, a designed path-based model is developed. A Benders-and-Price algorithm by combining the Benders decomposition and column generation is proposed to solve the LP-relaxation of the path-based model, and a bespoke Branch-and-Price is used to obtain the integer solution. Numerical experiments indicate that a variable timetable approach can reduce the required fleet size with a tolerable timetable deviation in comparison with a fixed timetable approach. Moreover, the proposed algorithm is greatly superior to GUROBI in terms of computational efficiency and guarantees the quality of the solution.

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Section: Discussionmentioning

confidence: 99%

Section: Solution Methodsmentioning

confidence: 99%

Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach

Lan

Song

et al. 2019

Journal of Advanced Transportation

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“…This approach has been applied to other integrated problems in transportation, such as aircraft routing and crew scheduling problem [20], and vehicle scheduling based on a variable timetable problem [21]. For more literature about this approach, we refer the reader to Mercier et al [22], Restrepo et al [23], and Lee and Han [24]. For the details on Benders decomposition and column generation, readers are referred to Costa [25] and Barnhart et al [26], respectively.…”

Section: Solution Methods For Model M2mentioning

confidence: 99%

“…where the objective function ( 22) is to minimize the total cost as Eq. (1) expresses; Constraints (23) indicate that each shipment select exactly one block path; Constraints ( 24)-( 27) are corresponding to Constraints ( 4)-( 7), respectively, and Constraints (30) are corresponding to Constraints (8). Constraints ( 28) and ( 29) are the track number constraints as Constraints ( 9) express.…”

Section: A the Arc-based Modelmentioning

confidence: 99%

Optimizing Train Formation Problem With Car Flow Routing and Train Routing by Benders-and-Price Approach

Lan

et al. 2019

IEEE Access

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As the core of the rail freight flow organization process, train formation problem (TFP) has attracted much attention. In Chinese practice, car flow routing, TFP, and train routing are usually optimized sequentially to reduce the complexity of computation, which may result in a local optimum, and even no feasible solution. To address this issue, this paper studies the integrated optimization of the three sub problems with aims to minimize the total cost of transportation cost, accumulation cost, and classification cost. An integer linear arc-based model incorporating the unitary and in-tree rules of a shipment is first formulated and solved by the state-of-the-art solver GUROBI. Since GUROBI can't deal with the large test cases, a path-based model is built and solved by a bespoken two-phase algorithm. The first phase of the algorithm is Benders-and-Price approach that combines Benders decomposition and column generation, and the second phase is to solve the arc-based model with some variables fixed as the corresponding values fetched from the first phase. The results show that the proposed algorithm outperforms GUROBI, and the acceleration techniques, i.e., trust region and Pareto-optimal cuts, can improve the convergence efficiency of Benders decomposition significantly.INDEX TERMS Train formation problem, car flow routing, train routing, benders decomposition, column generation.

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“…There is also an application to feature-based assembly planning [71]. Employee scheduling applications include shift selection and task sequencing [9], multi-activity shift scheduling [106], shift scheduling with fairness constraints [37], railway crew rostering with fairness constraints [87], and a multi-activity tour scheduling problem that integrates shift scheduling with days-off planning [96].…”

Section: Shop Factory and Employee Schedulingmentioning

confidence: 99%

Logic-Based Benders Decomposition for Large-Scale Optimization

Hooker

2019

Springer Optimization and Its Applications

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Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming problem. It is amenable to a wide variety large-scale problems that decouple or otherwise simplify when certain decision variables are fixed. This chapter presents the basic theory of LBBD and explains how classical Benders decomposition is a special case. It also describes branch and check, a variant of LBBD that solves the master problem only once. It illustrates in detail how Benders cuts and subproblem relaxations can be developed for some planning and scheduling problems. It then describes the role of LBBD in three large-scale case studies. The chapter concludes with an extensive survey of the LBBD literature, organized by problem domain, to allow the reader to explore how Benders cuts have been developed for a wide range of applications.

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Combining Benders decomposition and column generation for multi-activity tour scheduling

Cited by 16 publications

References 36 publications

Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach

Optimizing Vehicle Scheduling Based on Variable Timetable by Benders-and-Price Approach

Optimizing Train Formation Problem With Car Flow Routing and Train Routing by Benders-and-Price Approach

Logic-Based Benders Decomposition for Large-Scale Optimization

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