Multi-start heuristics for the Two-Echelon Vehicle Routing Problem

In this paper we address the Two-Echelon Vehicle Routing Problem (2E-VRP), an extension of the classical Capacitated VRP, where the delivery from a single depot to the customers is managed by routing and consolidating the freight through intermediate depots called satellites. We present a family of Multi-Start heuristics based on separating the depot-to-satellite transfer and the satellite-to-customer delivery by iteratively solving the two resulting routing subproblems, while adjusting the satellite workloads that link them. The common scheme on which all the heuristics are based consists in, after having found an initial solution, applying a local search phase, followed by a diversification; if the new obtained solutions are feasible, then local search is applied again, otherwise a feasibility search procedure is applied, and if it successful, the local search is applied on the newfound solution. Different diversification strategies and feasibility search rules are proposed. We present computational results on a wide set of instances up to 50 customers and 5 satellites and compare them with results from the literature, showing how the new methods outperform previous existent methods, both in efficiency and accurac

The two-echelon capacitated vehicle routing problem: models and math-based heuristics

Multiechelon distribution systems are quite common in supply-chain and logistics. They are used by public administrations in their transportation and traffic planning strategies, as well as by companies, to model own distribution systems. In the literature, most of the studies address issues relating to the movement of flows throughout the system from their origins to their final destinations. Another recent trend is to focus on the management of the vehicle fleets required to provide transportation among different echelons. The aim of this paper is twofold. First, it introduces the family of two-echelon vehicle routing problems (VRPs), a term that broadly covers such settings, where the delivery from one or more depots to customers is managed by routing and consolidating freight through intermediate depots. Second, it considers in detail the basic version of two-echelon VRPs, the two-echelon capacitated VRP, which is an extension of the classical VRP in which the delivery is compulsorily delivered through intermediate depots, named satellites. A mathematical model for two-echelon capacitated VRP, some valid inequalities, and two math-heuristics based on the model are presented. Computational results of up to 50 customers and four satellites show the effectiveness of the methods developed

A Reactive GRASP with Path Relinking for the Two-Echelon Vehicle Routing Problem

We propose a meta-heuristic based on GRASP combined with Path Relinking to address the Two-Echelon Vehicle Routing Problem, an extension of the Capacitated Vehicle Routing Problem in which the delivery from a single depot to customers is achieved by routing and consolidating the freight through intermediate depots called satellites. The problem is treated by separating the depot-to-satellite transfer and the satellite-to-customer delivery, and iteratively solving the two resulting routing subproblems, while adjusting the satellite workloads that link them. The meta-heuristic scheme consists of applying a GRASP and a local search procedures in sequence. Then, the resulting solution is linked to an elite solution by means of a Path Relinking procedure. To escape from infeasible solutions, which are quite common in this kind of problem, a feasibility search procedure is applied within Path Relinking. Extensive computational results on instances with up to 50 customers and 5 satellites show that the meta-heuristic is able to improve literature results, both in efficiency and accurac

A case study of two-echelon multi-depot vehicle routing problem

The Vehicle Routing Problem (VRP) is a classic combinatorial optimization problem and a topic still studied for practical applications. Current research focuses on single echelon distribution systems such as distribution centers serving customers. However, in typical distribution, goods flows among regional distribution centers, local warehouses and customers, defined as a two-echelon network. The two-echelon multiple depot VRP problem is documented and applied to two stages illustrated by a small scale computational example. In the first stage, the simulated annealing algorithm is employed to determine the routes between local warehouses and final customers. For the second stage, trial-and-error is applied to obtain the number and location of regional distribution centers and the routes between regional distribution centers and local warehouses. Matlab is utilized to simulate annealing iterations and cost functions are analyzed. The convergence tendency of simulated annealing is depicted in figures by Matlab coding. Contributions include demonstration between the SA algorithm and a specific combinatorial optimization problem, and an application of the algorithm

Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model

This article introduces a sustainable integrated bi-objective location-routing model, its two-phase solution approach and an analysis procedure for the distribution side of three-echelon logistics networks. The mixed-integer programming model captures several real-world factors by introducing an additional objective function and a set of new constraints in the model that outbound logistics channels find difficult to reconcile. The sustainable model minimises CO2 emissions from transportation and total costs incurred in facilities and the transportation channels. Design of Experiment (DoE) is integrated to the meta-heuristic based optimiser to solve the model in two phases. The DoE-guided solution approach enables the optimiser to offer the best stable solution space by taking out solutions with poor design features from the space and refining the feasible solutions using a convergence algorithm thereby selecting the realistic results. Several alternative solution scenarios are obtained by prioritising and ranking the realistic solution sets through a multi-attribute decision analysis tool, Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The robust model provides the decision maker the ability to take decisions on sustainable open alternative optimal routes. The outcomes of this research provide theoretical and methodological contributions, in terms of integrated bi-objective location-routing model and its two-phase DoE-guided meta-heuristic solution approach, for the distribution side of three-echelon logistics networks

Strategies for dynamic appointment making by container terminals

We consider a container terminal that has to make appointments with barges dynamically, in real-time, and partly automatic. The challenge for the terminal is to make appointments with only limited knowledge about future arriving barges, and in the view of uncertainty and disturbances, such as uncertain arrival and handling times, as well as cancellations and no-shows. We illustrate this problem using an innovative implementation project which is currently running in the Port of Rotterdam. This project aims to align barge rotations and terminal quay schedules by means of a multi-agent system. In this\ud paper, we take the perspective of a single terminal that will participate in this planning system, and focus on the decision making capabilities of its intelligent agent. We focus on the question how the terminal operator can optimize, on an operational level, the utilization of its quay resources, while making reliable appointments with barges, i.e., with a guaranteed departure time. We explore two approaches: (i) an analytical approach based on the value of having certain intervals within the schedule and (ii) an approach based on sources of exibility that are naturally available to the terminal. We use simulation to get insight in the benefits of these approaches. We conclude that a major increase in utilization degree could be achieved only by deploying the sources of exibility, without harming the waiting time of barges too much