Heuristics for multi-attribute vehicle routing problems: A survey and synthesis

Vidal, Thibaut; Crainic, Teodor Gabriel; Gendreau, Michel; Prins, Christian

doi:10.1016/j.ejor.2013.02.053

Cited by 349 publications

(202 citation statements)

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“…The column generation subproblem uses the reduced costs to extend I and verify optimality, similarly to the simplex method, as described above. Given an optimal extreme point to the restricted master problem, using the corresponding optimal solution π * to its linear programming 3 The reduced costs are de ned in Appendix B.1. 4 For a linear program on the form (1) with n ≥ m, it holds that every extreme point corresponds to at most m non-zero variable values x i , i = 1, .…”

Section: (3c)mentioning

confidence: 99%

“…Evaluation of xed sequences, including time windows where each customer needs to be serviced within a given time-frame, networks with timedependent features such as time-dependent travel times or time-dependent service costs, and 2D and 3D loading constraints. [3] Many di erent solution methods, both exact and heuristic, have been developed for di erent types of vehicle routing problems, and even though the methods need to be tailored to the speci c problem, several methods can be applied to di erent extensions of cVRP. Consistently, exact methods for vehicle routing problems can only solve problems with up to 200 customers (see [3,10,18]).…”

Section: Benders' Decompositionmentioning

confidence: 99%

“…There is a growing industry of software for transportation planning based on methods developed by the scienti c community for vehicle routing problems, and increasingly complex models and larger sized problems are solved ( [3]). In this thesis, the focus is on nding models and algorithms appropriate for vehicle routing problems with a very large set of vehicle types.…”

Section: Introductionmentioning

confidence: 99%

“…The cheapest path from node 1 to node 5, disregarding resource consumption, is (1,2,3,5), with the associated cost C (1,2,3,5) = 0.43. However, the path (1, 2, 3, 5) is not resource feasible, since T 1 5 (1,2,3,5) = 22 > 20.…”

mentioning

confidence: 99%

“…However, the path (1, 2, 3, 5) is not resource feasible, since T 1 5 (1,2,3,5) = 22 > 20. The cheapest (shortest) path from node 1 to node 5, that is also resource feasible, is (1,3,5), with the cost C (1,3,5) = 0.88. For this example, dynamic programming is not very useful since the optimal path can be found easily by inspection.…”

mentioning

confidence: 99%

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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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Section: (3c)mentioning

confidence: 99%