A Branch and Cut method for the Capacitated Location-Routing Problem

Belenguer, José Manuel; Benavent, Enrique; Prins, Christian; Prodhon, Caroline; Calvo, Roberto Wolfler

doi:10.1109/icsssm.2006.320765

Cited by 48 publications

(83 citation statements)

References 15 publications

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“…Belenguer et al [5] introduced a two-index integer programming formulation and families of valid inequalities. They were able to solve instances with up to 50 customers.…”

Section: Literature Reviewmentioning

confidence: 99%

An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics

Hemmelmayr

Cordeau

Crainic

2012

Computers & Operations Research

380

170

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In this paper, we propose an adaptive large neighborhood search heuristic for the Two-Echelon Vehicle Routing Problem (2E-VRP) and the Location Routing Problem (LRP). The 2E-VRP arises in two-level transportation systems such as those encountered in the context of city logistics. In such systems, freight arrives at a major terminal and is shipped through intermediate satellite facilities to the final customers. The LRP can be seen as a special case of the 2E-VRP in which vehicle routing is performed only at the second level. We have developed new neighborhood search operators by exploiting the structure of the two problem classes considered and have also adapted existing operators from the literature. The operators are used in a hierarchical scheme reflecting the multi-level nature of the problem. Computational experiments conducted on several sets of instances from the literature show that our algorithm outperforms existing solution methods for the 2E-VRP and achieves excellent results on the LRP.

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“…Belenguer et al [5] introduced a two-index integer programming formulation and families of valid inequalities. They were able to solve instances with up to 50 customers.…”

Section: Literature Reviewmentioning

confidence: 99%

An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics

Hemmelmayr

Cordeau

Crainic

2012

Computers & Operations Research

380

170

View full text Add to dashboard Cite

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“…This effect can be seen when analyzing clustered instances such as the ones described in Belenguer et al. () and Akca et al. ().…”

Section: Analysis Of Resultsmentioning

confidence: 94%

Using horizontal cooperation concepts in integrated routing and facility‐location decisions

Quintero-Araújo

Gruler

Faulín

2017

Int Trans Operational Res

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In a global and competitive economy, efficient supply networks are essential for modern enterprises. Horizontal cooperation (HC) concepts represent a promising strategy to increase the performance of supply chains. HC is based on sharing resources and making joint decisions among different agents at the same level of the supply chain. This paper analyzes different cooperation scenarios concerning integrated routing and facility‐location decisions in road transportation: (a) a noncooperative scenario in which all decisions are individually taken (each enterprise addresses its own vehicle routing problem [VRP]); (b) a semicooperative scenario in which route‐planning decisions are jointly taken (facilities and fleets are shared and enterprises face a joint multidepot VRP); and (c) a fully cooperative scenario in which route‐planning and facility‐location decisions are jointly taken (also customers are shared, and thus enterprises face a general location routing problem). Our analysis explores how this increasing level of HC leads to a higher flexibility and, therefore, to a lower total distribution cost. A hybrid metaheuristic algorithm, combining biased randomization with a variable neighborhood search framework, is proposed to solve each scenario. This allows us to quantify the differences among these scenarios, both in terms of monetary and environmental costs. Our solving approach is tested on a range of benchmark instances, outperforming previously reported results.

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“…As a final conclusion to this section, we note that another set of undirected path elimination constraints is presented by Belenguer et al , however they are based on a different set of binary variables to model two‐node cycles. For this reason, a direct comparison between their inequalities and inequalities (30) and (31) is not straightforward and requires further investigation.…”

Section: Routing Problems With Multiple Depotsmentioning

confidence: 90%

“…This section is motivated by the formulations described in the two papers by Belenguer et al and Benavent and Martínez‐Sykora where no information is given on the value of the degree of the depot nodes. We first observe that solutions composed by chains such as

(d_{1}, i_{1}, \dots, i_{m}, d_{2})

, where

d_{1}

and

d_{2}

are two different depots and

i_{1}, \dots, i_{m}

are clients, are feasible for the models proposed by Belenguer et al and Benavent and Martínez‐Sykora without the path elimination constraints. However, such solutions are not feasible for the generic model proposed in Section 2 without the path elimination constraints, since the assignment constraints (1) and (2) require that, for each depot, the in‐degree and the out‐degree must be equal to one another.…”

Section: Routing Problems With Multiple Depotsmentioning

confidence: 99%

New path elimination constraints for multi‐depot routing problems

2017

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Multi‐depot routing problems arise in distribution logistics where a set of vehicles based at several depots are used to serve a number of clients. Most variants of this problem have the basic requirement that the route of each vehicle starts and ends at the same depot. This article describes new inequalities, namely multi‐cut constraints (MCC), which enforce this requirement in mathematical programming formulations of multi‐depot routing problems. The MCCs are exponential in size, and are equivalent to a compact three‐index formulation for the problem in terms of the associated linear programming relaxations. The article describes how a generalization of the MCCs can be obtained, in a similar manner, by using a stronger version of the three‐index formulation. The connection between the compact and the exponential formulations implies a separation procedure based on max‐flow/min‐cut computations, which has reduced complexity in comparison with a previously known set of constraints described for the same purpose. The new inequalities are used in a branch‐and‐cut algorithm. Computational results are presented for instances with up to 300 clients and 60 depots. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(3), 246–261 2017

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A Branch and Cut method for the Capacitated Location-Routing Problem

Cited by 48 publications

References 15 publications

An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics

An adaptive large neighborhood search heuristic for Two-Echelon Vehicle Routing Problems arising in city logistics

Using horizontal cooperation concepts in integrated routing and facility‐location decisions

New path elimination constraints for multi‐depot routing problems

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