Two-Echelon Capacitated Vehicle Routing Problem Research Articles

A Two-Echelon Capacitated Vehicle Routing Problem With Sharing Satellite Resources

A Two-Echelon Capacitated Vehicle Routing Problem With Sharing Satellite Resources

Two-echelon capacitated vehicle routing problem with grouping constraints and simultaneous pickup and delivery

This paper investigates the two-echelon capacitated vehicle routing problem with grouping constraints and simultaneous pickup and delivery (2E-VRPGS), which is a new variant of the classical two-echelon capacitated vehicle routing problem (2E-VRP). In the 2E-VRPGS, customers from the same administrative region are served by vehicles from the same satellite so as to ensure service consistency, with pickup and delivery being performed simultaneously in the second echelon. To solve this problem to optimality, we formulate it as a path-based model and develop a tailored branch-and-cut-and-price algorithm, which can also exactly solve two closely related variants of 2E-VRPGS in the literature: the 2E-VRP with grouping constraints (2E-VRPG), and the 2E-VRP with simultaneous pickup and delivery (2E-VRPS). In particular, a novel dominance rule in the labeling algorithm, together with several customized valid inequalities, has been put forward to effectively accelerate the solution method by exploiting the problem characteristics. To evaluate the efficacy of the proposed algorithm on the problems 2E-VRPG, 2E-VRPS, and 2E-VRPGS, extensive numerical experiments have been conducted on three types of benchmark instances. Computational results on the 2E-VRPGS show that our dominance rule can significantly reduce the number of generated labels and all families of valid inequalities have a great impact on strengthening the path-based model. The algorithm is found to be highly competitive when compared with the existing exact algorithm for the 2E-VRPG and some new findings and managerial insights are derived from sensitivity analysis.

A Branch-Cut-and-Price Approach for the Single-Trip and Multi-Trip Two-Echelon Vehicle Routing Problem with Time Windows

The paper studies the two-echelon capacitated vehicle routing problem with time windows, in which delivery of freight from depots to customers is performed using intermediate facilities called satellites. We consider the variant of the problem with precedence constraints for unloading and loading freight at satellites. In this variant allows for storage and consolidation of freight at satellites. Thus, the total transportation cost may decrease in comparison with the alternative variant with exact freight synchronization at satellites. We suggest a mixed integer programming formulation for the problem with an exponential number of route variables and an exponential number of precedence constraints that link first-echelon and second-echelon routes. Routes at the second echelon connecting satellites and clients may consist of multiple trips and visit several satellites. A branch-cut-and-price algorithm is proposed to solve efficiently the problem. This is the first exact algorithm in the literature for the multi-trip variant of the problem. We also present a postprocessing procedure to check whether the solution can be transformed to avoid freight consolidation and storage without increasing its transportation cost. It is shown that all single-trip literature instances solved to optimality admit optimal solutions of the same cost for both variants of the problem either with precedence constraints or with exact synchronization constraints. Experimental results reveal that our algorithm can be used to solve these instances significantly faster than another recent approach proposed in the literature.

A multi-commodity two-Echelon capacitated vehicle routing problem with time windows: Model formulations and solution approach

This paper studies the multi-commodity two-echelon capacitated vehicle routing problem with time windows. Specifically, we take customer-specific origin to destination, non-substitutable demands into account. The main components are: (i) first echelon tours, (ii) second echelon tours and (iii) movement of commodities from first echelon to second echelon, considering route connection and synchronization. Exploiting the structure of the problem, we propose a decomposition scheme which decouples the first and second echelon routing problems, by deleting the third component, and re-couples them by using constraints ensuring movement of commodities between the two echelons. Based on this decomposition, we present (i) a number of model formulations for the MC-2E-VRPTW, and (ii) develop an exact solution approach for this real-life problem. A computational study on a comprehensive set of instances shows the effectiveness in terms of computational effort and solution quality.

A parallelised large neighbourhood search heuristic for the asymmetric two-echelon vehicle routing problem with swap containers for cargo-bicycles

Cargo-bicycles are a promising alternative to conventional vans in city logistics in response to increasing urbanisation and environmental damage caused by city traffic. The delivery structure is modelled with the well studied Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP), which uses cross-docking from vans to cargo-bicycles at so-called satellites. To reduce the extra handling effort compared to single-tier systems, swap containers are used. Furthermore, for cargo-bicycles the consideration of asymmetric distance matrices is important. Therefore, we present the Asymmetric 2E-CVRP with Swap Containers and develop an efficient Parallelised Large Neighbourhood Search heuristic, that is further improved using a first-level heuristic. The heuristic is tested using the symmetric 2E-CVRP benchmark instances from the literature, outperforms previous heuristics for large instances and finds new best-known solutions. Subsequently, the heuristic is applied to a case study in Munich with 22 newly generated instances, each containing 200 customers and asymmetric distances. The results allow quantitative insights into the cost and CO2e emissions savings of the investigated cargo-bicycle set-up compared to conventional van delivery.

Simulated Annealing Algorithm for Multi Depot Two-Echelon Capacitated Vehicle Routing Problem

Although urban freight transport is a significant contributor to the development of a country, it has adverse effects on the environment and the quality of life in urban areas. To reduce these adverse effects, we can deploy sustainable city logistic strategies. Scheduling and routing of vehicles is a crucial decision in city logistic strategies. Hence, in this paper, we solve the Multi-Depot Two Echelon Capacitated Vehicle Routing Problem (MD2E-CVRP), which is a variant of Vehicle Routing Problem (VRP) with heterogeneous fleets at both levels. Since VRP is NP-hard, we have proposed a Simulated Annealing (SA) based heuristic solution algorithm and have tested it on the standard 2E- CVRP and MD2E-CVRP instances. The results obtained from SA have a good solution quality at just one-fiftieth of computational time using CPLEX and was found to be faster than Adaptive Large Neighborhood Search (ALNS) with only a marginal drop in solution quality.

An improved branch-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem

In the paper, we propose a branch-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem in which delivery of products from a depot to customers is performed using intermediate depots called satellites. Our algorithm incorporates significant improvements recently proposed in the literature for the standard capacitated vehicle routing problem such as bucket graph based labeling algorithm for the pricing problem, automatic stabilization, limited memory rank-1 cuts, and strong branching. In addition, we make some specific problem contributions. First, we introduce a new route based formulation for the problem which does not use variables to determine product flows in satellites. Second, we introduce a new branching strategy which significantly decreases the size of the branch-and-bound tree. Third, we introduce a new family of satellite supply inequalities, and we empirically show that it improves the quality of the dual bound at the root node of the branch-and-bound tree. Finally, extensive numerical experiments reveal that our algorithm can solve to optimality all literature instances with up to 200 customers and 10 satellites for the first time and thus double the size of instances which could be solved to optimality.

Branch-and-Price–Based Algorithms for the Two-Echelon Vehicle Routing Problem with Time Windows

This paper studies the two-echelon capacitated vehicle routing problem with time windows. The first echelon consists of transferring freight from depots to intermediate facilities (i.e., satellites), whereas the second echelon consists of transferring freight from these facilities to the final customers, within their time windows. We propose two path-based mathematical formulations for our problem: (1) in one formulation, paths are defined over both first- and second-echelon tours, and (2) in the other one, the first- and second-echelon paths are decomposed. Branch-and-price–based algorithms are developed for both formulations. We compare both formulations and solution methods on a comprehensive set of instances and are able to solve instances up to five satellites and 100 customers to optimality. This paper is the first paper in the literature that solves such large instance sizes. The online appendix is available at https://doi.org/10.1287/trsc.2018.0844 .

The two-echelon capacitated electric vehicle routing problem with battery swapping stations: Formulation and efficient methodology

In this paper, we present a two-echelon capacitated electric vehicle routing problem with battery swapping stations (2E-EVRP-BSS), which aims to determine the delivery strategy under battery driving range limitations for city logistics. The electric vehicles operating in the different echelons have different load capacities, battery driving ranges, power consumption rates, and battery swapping costs. We propose an integer programming formulation and a hybrid algorithm that combines a column generation and an adaptive large neighborhood search (CG-ALNS) to solve the problem. We conducted extensive computational experiments, demonstrate the applicability of the proposed model, and show the efficiency of the CG-ALNS algorithm. In addition, we explore the interplay between battery driving range and the effectiveness of vehicle emission reduction through sensitivity analysis.

New Valid Inequalities for the Two-Echelon Capacitated Vehicle Routing Problem

We introduce new valid inequalities for the two-echelon variant of the Capacitated Vehicle Routing Problem (CVRP)In particular, a first group of inequalities is obtained by extending to 2E-CVRP some of the most effective among the existing CVRP valid inequalities. A second group of inequalities is explicitly derived for the 2E-CVRP and concerns the flow feasibility at customer nodes and the satellite-customer route connectivity. The inequalities are then introduced in a Branch & Cut algorithm. Computational results show that the proposed algorithm is able both to solve to optimality many open literature instances and significantly reduce the optimality gap for the remaining instances.

A novel Dynamic programming approach for Two-Echelon Capacitated Vehicle Routing Problem in City Logistics with Environmental considerations

Abstract The paper proposes a Two-Echelon Capacitated Vehicle Routing Problem with Environmental consideration, intended for managing urban freight distribution in City Logistics. It presents a novel Dynamic programming approach that divides the main problem into several ones and uses an exact algorithm to obtain optimal route paths. The approach applies Fuzzy C-Means Clustering for assigning a group of customers to a satellite. The initial solution is improved with roulette selection, 2-opt, and Or-opt exchange heuristics. The approach was tested on benchmark instances, and obtained results are satisfactory. Moreover, the proposed method highlights the environmental improvement we can obtain in managing urban freight transportation.

A genetic-algorithm-based approach to the two-echelon capacitated vehicle routing problem with stochastic demands in logistics service

This paper addresses the two-echelon capacitated vehicle routing problem (2E-CVRP) with stochastic demands (2E-CVRPSD) in city logistics. A stochastic program with recourse is used to describe the problem. This program aims to minimize the sum of the travel cost and the expected cost of recourse actions resulting from potential route failures. In a two-echelon distribution system, split deliveries are allowed at the first level but not at the second level, thereby increasing the difficulty of calculating the expected failure cost. Three types of routes with or without split deliveries are identified. Different methods are devised or adapted from the literature to compute the failure cost. A genetic-algorithm-based (GA) approach is proposed to solve the 2E-CVRPSD. A simple encoding and decoding scheme, a modified route copy crossover operator, and a satellite-selection-based mutation operator are devised in this approach. The numerical results show that for all instances, the expected cost of the best 2E-CVRPSD solution found by the proposed approach is not greater than that of the best-known 2E-CVRP solution with an average relative gap of 2.57%. Therefore, the GA-based approach can find high-quality solutions for the 2E-CVRPSD.

A branch-and-cut algorithm for the two-echelon capacitated vehicle routing problem with grouping constraints

In this paper, we present a branch-and-cut algorithm for the two-echelon capacitated vehicle routing problem with grouping constraints (2E-CVRPGC), which is a new problem deriving from the classical two-echelon capacitated vehicle routing problem (2E-CVRP) by considering grouping constraints in the second echelon. Customers in the 2E-CVRPGC are divided into several disjoint groups, and the grouping constraints ensure that customers from the same group are served by vehicles from the same satellite. We formulate the problem as a mixed 0–1 linear program and propose five families of valid inequalities to strengthen the model. Based on the model and the inequalities, we implement a branch-and-cut algorithm to solve the problem. The proposed branch-and-cut algorithm was evaluated on two classes of randomly generated instances. The computational results show that the five families of valid inequalities can substantially improve the lower bounds yielded by the LP relaxation of the model, and the branch-and-cut algorithm can solve more instances to optimality than CPLEX. We also conduct additional experiments to analyze the impacts of the grouping constraints on the problem, and illustrate the differences between the 2E-CVRPGC and the 2E-CVRP.

Matheuristic for a two-echelon capacitated vehicle routing problem with environmental considerations in city logistics service

This paper addresses a two-echelon capacitated vehicle routing problem (2E-CVRP) with environmental considerations (2E-CVRP-E). A new arc-and-route-based mathematical model is constructed to formulate the problem in which the sum of drivers’ wage, fuel cost, and handling cost is minimized. A matheuristic based on variable neighborhood search (VNS) and integer programming is designed to solve the 2E-CVRP-E. The integer programming in the matheuristic is used as a post-optimization technique to find better solutions missed by the VNS algorithm or to construct the least-cost first-level routes. To validate its effectiveness, the matheuristic first performs tests on 2E-CVRP instances and improves 13 current best-known solutions out of 234 instances. Then it performs tests on the 2E-CVRP-E instances modified from the 2E-CVRP. For 2E-CVRP-E instances, the total cost of the best solution found by the matheuristic is smaller than that of the best-known 2E-CVRP solution with an average relative gap of 6.37%. Computational results prove that the proposed matheuristic can find high-quality solutions for the 2E-CVRP and the 2E-CVRP-E.

A new Bi-objective model for a Two-echelon Capacitated Vehicle Routing Problem for Perishable Products with the Environmental Factor

In multi-echelon distribution strategy freight is delivered to customers via intermediate depots. Rather than using direct shipments, this strategy is an increasingly popular one in urban logistics. This is primarily to alleviate the environmental (e.g., energy usage and congestion) and social (e.g., traffic-related air pollution, accidents and noise) consequences of logistics operations. This paper represents a two-echelon capacitated vehicle routing problem (2-ECVRP) in which customers' satisfaction and environmental issues are considered for perishable goods delivery for the first time. The paper proposes a novel bi-objective model that minimizes: 1) total customers waiting time, and 2) total travel cost. A restriction on maximum allowable carbon dioxide (CO2) emissions from transport in each route is considered as environmental issue in the problem. The proposed model is solved by simple additive weighting (SAW) method. Finally, the proposed model is applied to a real world problem in a supermarket chain. The results achieved by GAMS optimization software confirm the validity and high performance of the model in respect to the importance of the each objective function. Furthermore, the sensitivity analysis performed on the model reveals that less restrictive policies on carbon emissions lead to more total emissions but less total travel cost and customers waiting time.

Modelo matemático Two-echelon Capacitated Vehicle Routing Problem para a logística de distribuição de encomendas

Muitas cidades vêm enfrentando dificuldades de mobilidade urbana e, por isso estão impondo restrições para à circulação de caminhões de maior porte. Assim, empresas de logística vêm atuando em uma logística de dois níveis usando Centros de Distribuição Urbanos (CDU) que recebem caminhões de maior porte e fracionam a carga para distribuir aos clientes em caminhões de pequeno porte. Para colaborar com este planejamento, este artigo realiza uma adaptação de um modelo matemático baseado no Two-echelon Capacitated Vehicle Routing Problem (2E-CVRP) para resolver de forma integrada a formação de rotas entre o depósito central e os CDU e as rotas destes para os clientes. O modelo foi aplicado à logística dos Correios na região metropolitana do Espírito Santo e instâncias com até 4 CDU e 25 clientes foram testadas com o uso do solver CPLEX 12.6 obtendo as rotas para as entregas nos dois níveis.

A lower bound for the adaptive two-echelon capacitated vehicle routing problem

Adaptive two-echelon capacitated vehicle routing problem (A2E-CVRP) proposed in this paper is a variant of the classical 2E-CVRP. Comparing to 2E-CVRP, A2E-CVRP has multiple depots and allows the vehicles to serve customers directly from the depots. Hence, it has more efficient solution and adapt to real-world environment. This paper gives a mathematical formulation for A2E-CVRP and derives a lower bound for it. The lower bound is used for deriving an upper bound subsequently, which is also an approximate solution of A2E-CVRP. Computational results on benchmark instances show that the A2E-CVRP outperforms the classical 2E-CVRP in the costs of routes.

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

In this paper, we introduce a branch-and-cut-and-price algorithm for the two-echelon capacitated vehicle routing problem. The algorithm relies on a reformulation based on q-routes that combines two important features. First, it overcomes symmetry issues observed in a formulation coming from a previous study of the problem. Second, it is strengthened with several classes of valid inequalities. As a result, the branch-and-cut-and-price implementation compares favorably with previous exact solution approaches for the problem—namely, two branch-and-price algorithms and a branch-and-cut method. Overall, 10 new optimality certificates and 8 new best upper bounds are provided in this study. New best lower bounds are also presented for all instances in the hardest test set from the literature.

A Hybrid Approach to the Optimization of Multiechelon Systems

In freight transportation there are two main distribution strategies: direct shipping and multiechelon distribution. In the direct shipping, vehicles, starting from a depot, bring their freight directly to the destination, while in the multiechelon systems, freight is delivered from the depot to the customers through an intermediate points. Multiechelon systems are particularly useful for logistic issues in a competitive environment. The paper presents a concept and application of a hybrid approach to modeling and optimization of the Multi-Echelon Capacitated Vehicle Routing Problem. Two ways of mathematical programming (MP) and constraint logic programming (CLP) are integrated in one environment. The strengths of MP and CLP in which constraints are treated in a different way and different methods are implemented and combined to use the strengths of both. The proposed approach is particularly important for the discrete decision models with an objective function and many discrete decision variables added up in multiple constraints. An implementation of hybrid approach in theECLiPSesystem using Eplex library is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) and its variants are shown as an illustrative example of the hybrid approach. The presented hybrid approach will be compared with classical mathematical programming on the same benchmark data sets.

The time-dependent two-echelon capacitated vehicle routing problem with environmental considerations

Multi-echelon distribution strategy in which freight is delivered to customers via intermediate depots rather than using direct shipments is an increasingly popular strategy in urban logistics. This is primarily to alleviate the environmental (e.g., energy usage and congestion) and social (e.g., traffic-related air pollution, accidents and noise) consequences of logistics operations. This paper presents a comprehensive MILP formulation for a time-dependent two-echelon capacitated vehicle routing problem (2E-CVRP) that accounts for vehicle type, traveled distance, vehicle speed, load, multiple time zones and emissions. A case study in a supermarket chain operating in the Netherlands shows the applicability of the model to a real-life problem. Several versions of the model, each differing with respect to the objective function, are tested to produce a number of selected key performance indicators (KPIs) relevant to distance, time, fuel consumption and cost. The paper offers insight on economies of environmentally friendly vehicle routing in two-echelon distribution systems. The results suggest that an environmentally friendly solution is obtained from the use of a two-echelon distribution system, whereas a single-echelon distribution system provides the least-cost solution.