A unified solution framework for multi-attribute vehicle routing problems

Vehicle routing attributes are extra characteristics and decisions that complement the academic problem formulations and aim to properly account for real-life application needs. Hundreds of methods have been introduced in recent years for specific attributes, but the development of a single, general-purpose algorithm, which is both efficient and applicable to a wide family of variants remains a considerable challenge. Yet, such a development is critical for understanding the proper impact of attributes on resolution approaches, and to answer the needs of actual applications. This paper contributes towards addressing these challenges with a component-based design for heuristics, targeting multi-attribute vehicle routing problems, and an efficient general-purpose solver. The proposed Unified Hybrid Genetic Search metaheuristic relies on problem-independent unified local search, genetic operators, and advanced diversity management methods. Problem specifics are confined to a limited part of the method and are addressed by means of assignment, sequencing, and route-evaluation components, which are automatically selected and adapted and provide the fundamental operators to manage attribute specificities. Extensive computational experiments on 29 prominent vehicle routing variants, 42 benchmark instance sets and overall 1099 instances, demonstrate the remarkable performance of the method which matches or outperforms the current state-of-the-art problem-tailored algorithms. Thus, generality does not necessarily go against efficiency for these problem classes.     

Heuristics for multi-attribute vehicle routing problems: A survey and synthesis

The attributes of vehicle routing problems are additional characteristics or constraints that aim to better take into account the specificities of real applications. The variants thus formed are supported by a well-developed literature, including a large variety of heuristics. This article first reviews the main classes of attributes, providing a survey of heuristics and meta-heuristics for Multi-Attribute Vehicle Routing Problems (MAVRP). It then takes a closer look at the concepts of 64 remarkable meta-heuristics, selected objectively for their outstanding performance on 15 classic MAVRP with different attributes. This cross-analysis leads to the identification of “winning strategies” in designing effective heuristics for MAVRP. This is an important step in the development of general and efficient solution methods for dealing with the large range of vehicle routing variants.     

Heuristic solution approaches for the cumulative capacitated vehicle routing problem

Cumulative capacitated vehicle routing problem (CCVRP) is an extension of the well-known capacitated vehicle routing problem, where the objective is minimization of sum of the arrival times at nodes instead of minimizing the total tour cost. This type of routing problem arises when a priority is given to customer needs or dispatching vital goods supply after a natural disaster. This paper focuses on comparing the performances of neighbourhood and population-based approaches for the new problem CCVRP. Genetic algorithm (GA), an evolutionary algorithm using particle swarm optimization mechanism with GA operators, and tabu search (TS) are compared in terms of required CPU time and obtained objective values. In addition, a nearest neighbourhood-based initial solution technique is also proposed within the paper. To the best of authors’ knowledge, this paper constitutes a base for comparisons along with GA, and TS for further possible publications on the new problem CCVRP.     

City-courier routing and scheduling problems

This research seeks to propose innovative routing and scheduling strategies to help city couriers reduce operating costs and enhance service level. The strategies are realized by constructing a new type of routing and scheduling problem. The problem directly takes into account the inherent physical and operating constraints associated with riding in city distribution networks, which makes the problem involve multiple objectives and visiting specified nodes and arcs. Through network transformations, this study first formulates the city-courier routing and scheduling problem as a multi-objective multiple traveling salesman problem with strict time windows (MOMTSPSTW) that is NP-hard and new to the literature, and then proposes a multi-objective Scatter Search framework that seeks to find the set of Pareto-optimal solutions to the problem. Various new and improved sub-procedures are embedded in the solution framework. This is followed by an empirical study that shows and analyzes the results of applying the proposed method to a real-life city-courier routing and scheduling problem.     

An exact solution framework for a broad class of vehicle routing problems

This paper presents an exact solution framework for solving some variants of the vehicle routing problem (VRP) that can be modeled as set partitioning (SP) problems with additional constraints. The method consists in combining different dual ascent procedures to find a near optimal dual solution of the SP model. Then, a column-and-cut generation algorithm attempts to close the integrality gap left by the dual ascent procedures by adding valid inequalities to the SP formulation. The final dual solution is used to generate a reduced problem containing all optimal integer solutions that is solved by an integer programming solver. In this paper, we describe how this solution framework can be extended to solve different variants of the VRP by tailoring the different bounding procedures to deal with the constraints of the specific variant. We describe how this solution framework has been recently used to derive exact algorithms for a broad class of VRPs such as the capacitated VRP, the VRP with time windows, the pickup and delivery problem with time windows, all types of heterogeneous VRP including the multi depot VRP, and the period VRP. The computational results show that the exact algorithm derived for each of these VRP variants outperforms all other exact methods published so far and can solve several test instances that were previously unsolved.     

Guidelines for the computational testing of machine learning approaches to vehicle routing problems

Despite the extensive research efforts and the promising results obtained by the ML community on Vehicle Routing Problems, most of the proposed techniques are still seldom employed by the OR community. With the current work, we highlight a number of challenges arising during the computational evaluation of heuristics for VRPs. The resulting guidelines aim at defining a common testing setup for the approaches designed by the two communities, thus promoting and strengthening the collaboration between them.     

Multi-objective vehicle routing problems

Routing problems, such as the traveling salesman problem and the vehicle routing problem, are widely studied both because of their classic academic appeal and their numerous real-life applications. Similarly, the field of multi-objective optimization is attracting more and more attention, notably because it offers new opportunities for defining problems. This article surveys the existing research related to multi-objective optimization in routing problems. It examines routing problems in terms of their definitions, their objectives, and the multi-objective algorithms proposed for solving them.     

Computing inter-site distances for routing and scheduling problems

Routing and scheduling problems have received considerable attention in the literature in terms of model building and algorithm development. On these fronts, progress has been substantial. However, one often neglected (yet critical) aspect concerning the use of these models and algorithms is their data requirements. In particular, the distance matrix yielding the shortest distance between each pair of sites (nodes) represents a major portion of the data required by all such problems. Yet, such data are seldom available with the degree of accuracy desired and often are not available at all.This paper describes an efficient method for obtaining this distance matrix that is based on the underlying road structure for the geographic region in question. Thus, the distances obtained reflect ‘actual’ distances. Finally, the paper presents some brief computational experience and discusses an implementation concerning the routing of environmental inspectors in the state of Pennsylvania.     

A branch-and-cut algorithm for vehicle routing problems

We present a branch-and-cut algorithm for the identical customer Vehicle Routing Problem. Transforming the problem into an equivalent Path-Partitioning Problem allows us to exploit its polyhedral structure and to generate strong cuts corresponding to facet-inducing inequalities. By using cuts defined by multistars, partial multistars and generalized subtour elimination constraints, we are able to consistently solve 60-city problems to proven optimality and are currently attempting to solve problems involving a hundred cities. We also present details of the computer implementation and our computational results.     

Iterated local search for workforce scheduling and routing problems

The integration of scheduling workers to perform tasks with the traditional vehicle routing problem gives rise to the workforce scheduling and routing problems (WSRP). In the WSRP, a number of service technicians with different skills, and tasks at different locations with pre-defined time windows and skill requirements are given. It is required to find an assignment and ordering of technicians to tasks, where each task is performed within its time window by a technician with the required skill, for which the total cost of the routing is minimized. This paper describes an iterated local search (ILS) algorithm for the WSRP. The performance of the proposed algorithm is evaluated on benchmark instances against an off-the-shelf optimizer and an existing adaptive large neighbourhood search algorithm. The proposed ILS algorithm is also applied to solve the skill vehicle routing problem, which can be viewed as a special case of the WSRP. The computational results indicate that the proposed algorithm can produce high-quality solutions in short computation times.     

Integer linear programming formulation for vehicle routing problems

A recently proposed integer linear programming formulation for the vehicle routing proglems is found to have an error; in particular the distance constraint described is not sufficiently restrictive.     

Integrated machine scheduling and vehicle routing with time windows

This paper integrates production and outbound distribution scheduling in order to minimize total tardiness. The overall problem consists of two subproblems. The first addresses scheduling a set of jobs on parallel machines with machine-dependent ready times. The second focusses on the delivery of completed jobs with a fleet of vehicles which may differ in their loading capacities and ready times. Job-dependent processing times, delivery time windows, service times, and destinations are taken into account. A genetic algorithm approach is introduced to solve the integrated problem as a whole. Two main questions are examined. Are the results of integrating machine scheduling and vehicle routing significantly better than those of classic decomposition approaches which break down the overall problem, solve the two subproblems successively, and merge the subsolutions to form a solution to the overall problem? And if so, is it possible to capitalize on these potentials despite the complexity of the integrated problem? Both questions are tackled by means of a numerical study. The genetic algorithm outperforms the classic decomposition approaches in case of small-size instances and is able to generate relatively good solutions for instances with up to 50 jobs, 5 machines, and 10 vehicles.     

Solving symmetric vehicle routing problems asymmetrically

The vehicle routing problem can be regarded as a traveling salesman problem with additional constraints. Algorithms based on assignment relaxations provide better solutions for the symmetric traveling salesman problem if they are used on an asymmetric transformed distance matrix, as shown by Jonker et al., in a paper in Operations Research. The generalization of such a transformation to the distance matrix of symmetric vehicle routing problems is described. The approach is illustrated within a heuristic algorithm, although it can also be the basis for an exact algorithm. For a number of standard problems computational results are given, that are competitive to results of other algorithms.     

A solution approach for dynamic vehicle and crew scheduling

In this paper, we discuss the dynamic vehicle and crew scheduling problem and we propose a solution approach consisting of solving a sequence of optimization problems. Furthermore, we explain why it is useful to consider such a dynamic approach and compare it with a static one. Moreover, we perform a sensitivity analysis on our main assumption that the travel times of the trips are known exactly a certain amount of time before actual operation.We provide extensive computational results on some real-world data instances of a large public transport company in the Netherlands. Due to the complexity of the vehicle and crew scheduling problem, we solve only small and medium-sized instances with such a dynamic approach. We show that the results are good in the case of a single depot. However, in the multiple-depot case, the dynamic approach does not perform so well. We investigate why this is the case and conclude that the fact that the instance has to be split in several smaller ones, has a negative effect on the performance.     

Design of an IT-driven decision support system for vehicle routing and scheduling

This paper presents the development of a decision support system used by an oil downstream company for routing and scheduling purposes. The studied problem refers to a complex delivery process of oil products from a number of distribution centers to all customers. The latest rapid advance of operations research (OR) applications, in the form of advanced planning and scheduling (APS) systems, has shown that OR algorithms can be applied in practice if (a) they are embodied in packaged information technology (IT) solutions, (b) the interface problems to mainstream ERP software applications are solved. In this study the utilisation of advanced IT systems supports effectively the planning and management of distribution operations. The combination of a supply chain management (SCM) application with a geographical information system (GIS) integrated with an enterprise resource planning (ERP) software resulted to this innovative decision support tool. The objectives of this new tool are: optimum use of the distribution network resources, transportation cost reduction and customer service improvement. The paper concludes with the benefits of the new system, emphasising at how new technologies can support transportation processes with the help of operations research algorithms embedded in software applications.     

A tabu search algorithm for the multi-trip vehicle routing and scheduling problem

This paper describes a novel tabu search heuristic for the multi-trip vehicle routing and scheduling problem (MTVRSP). The method was developed to tackle real distribution problems, taking into account most of the constraints that appear in practice. In the MTVRSP, besides the constraints that are common to the basic vehicle routing problem, the following ones are present: during each day a vehicle can make more than one trip; the customers impose delivery time windows; the vehicles have different capacities considered in terms of both volume and weight; the access to some customers is restricted to some vehicles; the drivers' schedules must respect the maximum legal driving time per day and the legal time breaks; the unloading times are considered.     

A savings based method for real-life vehicle routing problems

This paper describes a Savings Based algorithm for the Extended Vehicle Routing Problem. This algorithm is compared with a sequential insertion algorithm on real-life data. Besides the traditional quality measures such as total distance travelled and total workload, we compare the routing plans of both algorithms according to non-standard quality measures that help to evaluate the ‘visual attractiveness’ of the plan. Computational results show that, in general, the savings based algorithm not only performs better with respect to these non-standard quality measures, but also with respect to the traditional measures.     

Metaheuristics for vehicle routing problems with three-dimensional loading constraints

This paper addresses an important combination of three-dimensional loading and vehicle routing, known as the Three-Dimensional Loading Capacitated Vehicle Routing Problem. The problem calls for the combined optimization of the loading of freight into vehicles and the routing of vehicles along a road network, with the aim of serving customers with minimum traveling cost. Despite its clear practical relevance in freight distribution, the literature on this problem is very limited. This is because of its high combinatorial complexity.