A robust branch‐cut‐and‐price algorithm for the heterogeneous fleet vehicle routing problem

Pessoa, Artur Alves; Uchôa, Eduardo; AragÃ£o, Marcus Poggi de

doi:10.1002/net.20330

Cited by 56 publications

(33 citation statements)

References 16 publications

(38 reference statements)

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“…Two di erent approaches have been used to solve (22) in this thesis, one using AMPL and CPLEX, and one using dynamic programming in Matlab. Both approaches have been implemented in such a way that the solution algorithm can be interrupted before an optimal solution to the subproblem has been found, either when a prede ned time limit has been exceeded, or after a certain number of routes with negative reduced cost has been found.…”

Section: Subproblemmentioning

confidence: 99%

“…Below, two mathematical formulations of the problem (22) are presented; these can be directly implemented in AMPL and CPLEX. The model (23) has been adapted to the column generation subproblem (22), using the ow formulation (12) of hVRP.…”

Section: Mathematical Formulations Implemented In Ampl and Cplexmentioning

confidence: 99%

“…The model (23) has been adapted to the column generation subproblem (22), using the ow formulation (12) of hVRP. The constraints (23c) (23e) have been added, and the constraints (12d) (12g) have been replaced with the constraints (23f) (23h).…”

Section: Mathematical Formulations Implemented In Ampl and Cplexmentioning

confidence: 99%

“…We have adapted the formulation of the VRP with wime windows [32, p. 58] which employs variables representing time instead of ow variables for the column generation subproblem (22). Here the variables e ij and the constraints (23f) (23g) are replaced by the variables s i , i ∈ N , (representing order with respect to time) and…”

Section: Mathematical Formulations Implemented In Ampl and Cplexmentioning

confidence: 99%

“…Further, the alternative constraints make the constraints (23c) redundant; they are not included in the formulation in [32, p. 58]. However, they strengthen the formulation (in terms of a tighter representation of the convex hull of the set of feasible solutions) and according to the following paragraph yield great improvements in solution time when applied to the subproblem (22).…”

Section: Mathematical Formulations Implemented In Ampl and Cplexmentioning

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: Subproblemmentioning

confidence: 99%

Section: Mathematical Formulations Implemented In Ampl and Cplexmentioning

confidence: 99%

Section: Mathematical Formulations Implemented In Ampl and Cplexmentioning

confidence: 99%

Section: Mathematical Formulations Implemented In Ampl and Cplexmentioning

confidence: 99%

Section: Mathematical Formulations Implemented In Ampl and Cplexmentioning

confidence: 99%

See 3 more Smart Citations

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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A branch‐and‐price‐and‐cut algorithm for the truck‐drone routing problem with simultaneously delivery and pickup

Li,

Ignatius,

Wang

et al. 2023

Naval Research Logistics

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Increasing environmental concerns and e‐commerce has attracted a growing focus on reverse logistics that not only delivers some goods to customers but also picks up other goods from customers. To achieve cost‐efficient and fast deliveries, integrating drones into the delivery and pickup services provides a competitive advantage, which however increases the operational challenges. We consider a truck‐drone routing problem with simultaneous delivery and pickup, where each truck carries a set of heterogeneous drones. Each truck can simultaneously perform its own delivery and pickup, and serve as an intermediate movable depot from which multiple drones can be dispatched to serve customers when the truck arrives at a customer, and the truck must wait until all the drones return. The energy consumption of drones is considered during their flights. All the delivery services must be performed, whereas the pickup services are optional with certain rewards. The objective is to find the synthetic‐routes of the truck‐drone combinations so as to minimize the sum of the assignment cost and the transport cost of the trucks and drones minus the total pickup revenue. To solve the problem, we devise a tailored branch‐and‐price‐and‐cut algorithm incorporating a specialized two‐stage bidirectional labeling algorithm to solve the challenging pricing problem. To enhance the efficiency of the algorithm, we use the subset‐row inequalities to tighten the lower bound, and apply some heuristic pricing strategies to quickly solve the pricing problem. We perform extensive numerical studies to assess the performance of the developed algorithm, analyze the merit of the truck‐drone cooperative service mode over the truck‐only service mode and the superiority of the configuration with heterogeneous drones, and ascertain the impacts of the key model parameters to generate managerial insights. We also show how our model would perform should it be used for the medical supply delivery and pickup in Shenzhen, China.

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Branch‐and‐cut algorithms for the vehicle routing problem with trailers and transshipments

Drexl

2013

Networks

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This article studies the vehicle routing problem with trailers and transshipments (VRPTT), a practically relevant, but challenging, generalization of the classical vehicle routing problem. The article makes three contributions: (i) Building on a nontrivial network representation, two mixed-integer programming formulations for the VRPTT are proposed. (ii) Based on these formulations, five different branch-and-cut algorithms are developed and implemented. (iii) The computational behavior of the algorithms is analyzed in an extensive computational study, using a large number of test instances designed to resemble real-world VRPTTs

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A robust branch‐cut‐and‐price algorithm for the heterogeneous fleet vehicle routing problem

Cited by 56 publications

References 16 publications

Modeling and Solving Vehicle Routing Problems with Many Available Vehicle Types

Modeling and Solving Vehicle Routing Problems with Many Available Vehicle Types

A branch‐and‐price‐and‐cut algorithm for the truck‐drone routing problem with simultaneously delivery and pickup

Branch‐and‐cut algorithms for the vehicle routing problem with trailers and transshipments

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