A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem

Hadjar, Ahmed; Marcotte, Odile; Soumis, François

doi:10.1287/opre.1050.0240

Cited by 97 publications

(69 citation statements)

References 13 publications

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“…Together with an integral solution this can be exploited to discard original binary variables with reduced cost larger than the optimality gap. Hadjar, Marcotte, and Soumis (2001) apply this technique to remove more than 90% of the flow variables in multiple depot vehicle scheduling problems.…”

Section: Pricing Out the Original X Variablesmentioning

confidence: 99%

Selected Topics in Column Generation

Lübbecke

Desrosiers

2005

Operations Research

835

488

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Dantzig-Wolfe decomposition and column generation, devised for linear programs, is a success story in large scale integer programming. We outline and relate the approaches, and survey mainly recent contributions, not yet found in textbooks. We emphasize the growing understanding of the dual point of view, which has brought considerable progress to the column generation theory and practice. It stimulated careful initializations, sophisticated solution techniques for the restricted master problem and subproblem, as well as better overall performance. Thus, the dual perspective is an ever recurring concept in our "selected topics."

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Section: Pricing Out the Original X Variablesmentioning

confidence: 99%

Selected Topics in Column Generation

Lübbecke

Desrosiers

2005

Operations Research

835

488

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“…The problem has some similarities with the multiple-depot vehicle scheduling problem (see, e.g., [18,8]), which however has two remarkable differences with respect to our problem. First, each vehicle must depart from a depot and go back to the same depot at the end of the day, which makes the problem hard, whereas in our case each TU (or locomotive/car) goes back to its original depot only after a certain number of days, generally not specified in advance.…”

Section: Literature Reviewmentioning

confidence: 99%

Solving a real-world train-unit assignment problem

2010

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Abstract. We face a real-world train unit assignment problem for an operator running trains in a regional area. Given a set of timetabled train trips, each with a required number of passenger seats, and a set of train units, each with a given number of available seats, the problem calls for an assignment of the train units to trips, possibly combining more than one train unit for a given trip, that fulfills the seat requests. With respect to analogous case studies previously faced in the literature, ours is characterized by the fairly large number of distinct train unit types available (in addition to the fairly large number of trips to be covered). As a result, although there is a wide margin of improvement over the solution used by the practitioners (as our results show), even only finding a solution of the same value is challenging in practice. We present a successful approach, based on an ILP formulation in which the seat requirement constraints are stated in a ")-1(strong" fo rm, derived from the description of the convex hull of the variant of the knapsack polytope arising when the sum of the variables is restricted not to exceed two, illustrating computational results on our case study.

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“…Constraints (11) ensure that all jobs are processed and Constraints (12) guarantee that only the edge (i, j) with x i,j = 1 is allowed for workers to traverse. Constraints (13)- (15) are equivalent to Constraints (6)- (8), respectively.…”

Section: Set-covering Modelmentioning

confidence: 99%

“…As Constraints (13) and (14) can be fully ensured by our proposed valid inequalities and branching strategies, we do not need to add them into the formulation. Therefore, we construct the master problem using objective function (10) and Constraints (11) and (16)- (17). The linear relaxation of the master problem (LMP) provides a lower bound for the original problem.…”

Section: Branch-and-price-and-cut Algorithmmentioning

confidence: 99%

Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints

Luo

Qin

Zhu

et al. 2016

Naval Research Logistics

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Abstract:In this article, we propose a branch-and-price-and-cut (BPC) algorithm to exactly solve the manpower routing problem with synchronization constraints (MRPSC). Compared with the classical vehicle routing problems (VRPs), the defining characteristic of the MRPSC is that multiple workers are required to work together and start at the same time to carry out a job, that is, the routes of the scheduling subjects are dependent. The incorporation of the synchronization constraints increases the difficulty of the MRPSC significantly and makes the existing VRP exact algorithm inapplicable. Although there are many types of valid inequalities for the VRP or its variants, so far we can only adapt the infeasible path elimination inequality and the weak clique inequality to handle the synchronization constraints in our BPC algorithm. The experimental results at the root node of the branch-and-bound tree show that the employed inequalities can effectively improve the lower bound of the problem. Compared with ILOG CPLEX, our BPC algorithm managed to find optimal solutions for more test instances within 1 hour.

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A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem

Cited by 97 publications

References 13 publications

Selected Topics in Column Generation

Selected Topics in Column Generation

Solving a real-world train-unit assignment problem

Branch‐and‐price‐and‐cut for the manpower routing problem with synchronization constraints

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