A Unified Framework for Deterministic Time Constrained Vehicle Routing and Crew Scheduling Problems

Desaulniers, Guy; Desrosiers, Jacques; loachim, Irina; Solomon, Marius M.; Soumis, François; Villeneuve, Daniel L.

doi:10.1007/978-1-4615-5755-5_3

Cited by 161 publications

(126 citation statements)

References 72 publications

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“…However, X could have a much more complicated non-linear definition (Desaulniers et al, 1998). We assume that z be finite.…”

Section: Decomposition Of Integer Programssupporting

confidence: 42%

“…Their general branching strategy works on the variables of the compact formulation. Multicommodity flow formulations for various applications of vehicle routing and crew scheduling proposed by Desaulniers et al (1998) follow this scheme. For the classical cutting stock problem (4), the above procedure leads to Kantorovich's formulation (1960) where a commodity is defined for each (identical) available roll.…”

Section: Column Generation For Integer Programsmentioning

confidence: 43%

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Selected Topics in Column Generation

Lübbecke

Desrosiers

2005

Operations Research

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815

484

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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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“…However, X could have a much more complicated non-linear definition (Desaulniers et al, 1998). We assume that z be finite.…”

Section: Decomposition Of Integer Programssupporting

confidence: 42%

Section: Column Generation For Integer Programsmentioning

confidence: 43%

Selected Topics in Column Generation

Lübbecke

Desrosiers

2005

Operations Research

Self Cite

815

484

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“…with the particular choice of optimal solution (π * , q * ) to (40) given by (43). Thus, nding the variable α p , p ∈ P \ P, with minimal reduced cost amounts to solving the column generation subproblem (41).…”

Section: B1 Linear Programsupporting

confidence: 41%

“…Set partitioning formulations can be related to more compact formulations, such as the ow formulation (12), using Dantzig-Wolfe decompositions. A decomposition for a more complex problem including time windows, multiple depots, split deliveries, and pickups and deliveries of which hVRP is a special case, is found in [43]. Another decomposition is found in [44] for the vehicle routing problem with time windows and a xed number of vehicles, resulting in one subproblem for each vehicle.…”

Section: B2 Binary Programcontrasting

confidence: 37%

“…Any vector (π,γ) that satis es the conditions 1.π is an extreme point to the set π ∈ R |N0| π satis es (30b) , 2.γ k = 0, k ∈ K( y), and 3.γ k = γ * k where γ * k is optimal in (Gamma(k,π)), for k ∈ K \ K( y), is an extreme point to the set F BendersSPDual . 43 After solving (28a) (28b), (28d) the solution of which is optimal in Benders subproblem (BendersSP( y)), where the excluded variables are set to zero (x k r := 0, r ∈ R k , k ∈ K \ K( y)) using column generation, a value ofπ satisfying condition 1 of Claim 2 results from the last iteration. The important consequences of Claims 2 and 3 are the following: ifγ satis es conditions 2 and 3 of Claim 2, then (π,γ) is optimal in (BendersSPDual( y)).…”

Section: Optimal Extreme Point To Benders Subproblemmentioning

confidence: 42%

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Modeling and Solving Vehicle Routing Problems with Many Available Vehicle Types

Barman

Lindroth

Strömberg

2015

Springer Proceedings in Mathematics &Amp; Statistics

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In this thesis, models have been formulated and mathematical optimization methods developed for the heterogeneous vehicle routing problem with a very large set of available vehicle types, called many-hVRP. This is an extension of the standard heterogeneous vehicle routing problem (hVRP), in which typically fairly small sets of vehicle types are considered.Two mathematical models based on standard models for the hVRP have been formulated for the many-hVRP. Column generation and dynamic programming have been applied to both these models, following a successful algorithm for the hVRP. Benders' decomposition algorithm has also been applied to one of the models. In addition to the standard cost structure, where the cost of a pair of a vehicle and a route is determined by the length of the route and the vehicle type, we have studied costs that depend also on the load of the vehicle along the route. These load dependent costs were easily incorporated into the models, and other extensions could be similarly incorporated.By using a standard set of test instances (with between three and six vehicle types in each instance) we have been able to compare our implementation with published results for hVRP. For many-hVRP, we have extended these instances to include larger sets of vehicle types (with between 91 and 381 vehicle types in each instance). The results show that the algorithms implemented for the two models nd optimal solutions in a similar amount of time, but Benders' algorithm at times takes much longer to verify optimality. However, some other properties of Benders' algorithm suggests that it may constitute a good basis for a heuristic, when instances with even larger sets of vehicle types are used.

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The Vehicle Routing Problem with Time Windows: State‐of‐the‐Art Exact Solution Methods

Desaulniers

Desrosiers

Spoorendonk

2011

Wiley Encyclopedia of Operations Research and Management Science

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The vehicle routing problem with time windows (VRPTW) consists of finding least‐cost vehicle routes to service given customers exactly once each while satisfying the vehicle capacity and customer time windows. The VRPTW has been widely studied. We present here a short survey on the successful exact methods for solving it. These are branch‐cut‐and‐price algorithms, except the most efficient one which solves, by a mixed‐integer programming solver, a reduced set partitioning model obtained by performing variable elimination based on reduced cost. This method was able to solve all well‐known Solomon's benchmark instances except one, outperforming all the other algorithms previously published.

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A Unified Framework for Deterministic Time Constrained Vehicle Routing and Crew Scheduling Problems

Cited by 161 publications

References 72 publications

Selected Topics in Column Generation

Selected Topics in Column Generation

Modeling and Solving Vehicle Routing Problems with Many Available Vehicle Types

The Vehicle Routing Problem with Time Windows: State‐of‐the‐Art Exact Solution Methods

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