A Branch-and-Cut-and-Price Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem

Santos, Fernando Afonso; Mateus, Geraldo Robson; Cunha, Alexandre Salles da

doi:10.1287/trsc.2013.0500

Cited by 61 publications

(25 citation statements)

References 39 publications

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“…Different mathematical formulations have been proposed for the 2EVRP Jepsen et al, 2012;Santos et al, 2013Santos et al, , 2014 and for the 2ELRP (Boccia et al, 2011;Contardo et al, 2012). In this section, we display compact formulations based on the model of Cuda et al (2015).…”

Section: Mathematical Modelmentioning

confidence: 99%

A large neighbourhood based heuristic for two-echelon routing problems

Breunig

Schmid

Hartl

et al. 2016

Computers & Operations Research

113

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In this paper, we address two optimisation problems arising in the context of city logistics and two-level transportation systems. The two-echelon vehicle routing problem and the two-echelon location routing problem seek to produce vehicle itineraries to deliver goods to customers, with transits through intermediate facilities. To efficiently solve these problems, we propose a hybrid metaheuristic which combines enumerative local searches with destroy-and-repair principles, as well as some tailored operators to optimise the selections of intermediate facilities. We conduct extensive computational experiments to investigate the contribution of these operators to the search performance, and measure the performance of the method on both problem classes. The proposed algorithm finds the current best known solutions, or better ones, for 95% of the two-echelon vehicle routing problem benchmark instances. Overall, for both problems, it achieves high-quality solutions within short computing times. Finally, for future reference, we resolve inconsistencies between different versions of benchmark instances, document their differences, and provide them all online in a unified format

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Section: Mathematical Modelmentioning

confidence: 99%

A large neighbourhood based heuristic for two-echelon routing problems

Breunig

Schmid

Hartl

et al. 2016

Computers & Operations Research

113

View full text Add to dashboard Cite

show abstract

“…Jepsen et al (2012) described a branch-and-cut algorithm based on a new mathematical formulation and different valid inequalities. Exact algorithms were also designed by Baldacci et al (2013) and by Santos et al (2015). Santos et al described a branch-and-cut-and-price algorithm for the 2EVRP that relies on a reformulation based on the q-routes relaxation proposed for the capacitated vehicle routing problem (CVRP) by Christofides et al (1981).…”

Section: Related Literaturementioning

confidence: 99%

The electric two-echelon vehicle routing problem

Breunig

Baldacci

Hartl

et al. 2019

Computers & Operations Research

122

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Two-echelon distribution systems are attractive from an economical standpoint and help to keep large vehicles out of densely populated city centers. Large trucks can be used to deliver goods to intermediate facilities in accessible locations, whereas smaller vehicles allow to reach the final customers. Due to their reduced size, pollution, and noise, multiple companies consider using an electric fleet of terrestrial or aerial vehicles for last-mile deliveries.Route planning in multi-tier logistics leads to notoriously difficult problems. This difficulty is accrued in the presence of an electric fleet since each vehicle operates on a smaller range and may require planned visits to recharging stations. To study these challenges, we introduce the electric two-echelon vehicle routing problem (E2EVRP) as a prototypical problem. We propose a large neighborhood search (LNS) metaheuristic as well as an exact mathematical programming algorithm, which uses decomposition techniques to enumerate promising first-level solutions in conjunction with bounding functions and route enumeration for the second-level routes. These algorithms produce optimal or near-optimal solutions for the problem and allow us to evaluate the impact of several defining features of optimized battery-powered distribution networks.We created representative E2EVRP benchmark instances to simulate realistic metropolitan areas. In particular, we observe that the detour miles due to recharging decrease proportionally to 1/ρ x with x ≈ 5/4 as a function of the charging stations density ρ; e.g., in a scenario where the density of charging stations is doubled, recharging detours are reduced by 58%. Finally, we evaluate the trade-off between battery capacity and detour miles. This estimate is critical for strategic fleet-acquisition decisions, in a context where large batteries are generally more costly and less environment-friendly.

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“…For an introduction of VRP's exact solution algorithm, see [29][30][31]. Santos [32] proposed branch and bound algorithm and its solution to the weighted average method proposed by Santos [33] and Sahraeian, an extended version of 2E-VRP that includes two optimization goals, environmental costs and service satisfaction. However, the exact solution to the algorithm has poor adaptability to the customer scale, so the approximate solution algorithm is more favored by scholars when the problem scale is larger.…”

Section: Literature Reviewmentioning

confidence: 99%

Proactive Two-Level Dynamic Distribution Routing Optimization Based on Historical Data

Xue

Wen

2018

Mathematical Problems in Engineering

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In view of the dynamic dispersion of e-commerce logistics demand, this paper uses the historical distribution data of logistics companies to study data-driven proactive vehicle routing optimization. First, based on the classic 2E-VRP problem, a single-node/multistage 2E-VRP mathematical model is constructed. Then, a framework for solving the proactive vehicle routing optimization problem is proposed in combination with the characteristics of the proposed model, including four modules: data-driven demand forecasting methods, customer clustering methods, proactive demand quotas and replenishment strategies, and vehicle routing optimization procedure. The significant feature of the proposed solution framework is that the response to dynamic customers is proactive rather than passive. The solution is applied to the distribution practice of a large logistics company in Chongqing. The results show that the proposed method has better dynamic scene adaptability and customer response capabilities in traffic limit.

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A Branch-and-Cut-and-Price Algorithm for the Two-Echelon Capacitated Vehicle Routing Problem

Cited by 61 publications

References 39 publications

A large neighbourhood based heuristic for two-echelon routing problems

A large neighbourhood based heuristic for two-echelon routing problems

The electric two-echelon vehicle routing problem

Proactive Two-Level Dynamic Distribution Routing Optimization Based on Historical Data

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