A sweep-based algorithm for the fleet size and mix vehicle routing problem

This paper presents a new sweep-based heuristic for the fleet size and mix vehicle routing problem. This problem involves two kinds of decisions: the selection of a mix of vehicles among the available vehicle types and the routing of the selected fleet. The proposed algorithm first generates a large number of routes that are serviced by one or two vehicles. The selection of routes and vehicles to be used is then made by solving to optimality, in polynomial time, a set-partitioning problem having a special structure. Results on a set of benchmark test problems show that the proposed heuristic produces excellent solutions in short computing times. Having a fast but good solution method is needed for transportation companies that rent a significant part of their fleet and consequently can take advantage of frequent changes in fleet composition. Finally, the proposed heuristic produced new best-known solutions for three of the test problems; these solutions are reported.     

The capacitated arc routing problem with refill points

This article introduces the capacitated arc routing problem with refill points (CARP-RP). The vehicle servicing arcs must be refilled on the spot by using a second vehicle. The problem consists on simultaneously determining the vehicles routes that minimize the total cost. An integer linear programming model is proposed and tested.     

A deterministic tabu search algorithm for the fleet size and mix vehicle routing problem

The fleet size and mix vehicle routing problem consists of defining the type, the number of vehicles of each type, as well as the order in which to serve the customers with each vehicle when a company has to distribute goods to a set of customers geographically spread, with the objective of minimizing the total costs. In this paper, a heuristic algorithm based on tabu search is proposed and tested on several benchmark instances. The computational results show that the proposed algorithm produces high quality results within a reasonable computing time. Some new best solutions are reported for a set of test problems used in the literature.     

Scatter search for the fleet size and mix vehicle routing problem with time windows

This work proposes a scatter search (SS) approach to solve the fleet size and mix vehicle routing problem with time windows (FSMVRPTW). In the FSMVRPTW the customers need to be serviced in their time windows at minimal costs by a heterogeneous fleet. Computational results on 168 benchmark problems are reported. Computational testing revealed that our algorithm presented better results compared to other methods published in the literature.     

The periodic capacitated arc routing problem with irregular services

The aim of this paper is to introduce the periodic capacitated arc routing problem with irregular services. Some applications can be found in road maintenance operations and road network surveillance. The problem consists of determining a set of routes to cover a given network over a time horizon. The roads must be serviced a number of times in sub-periods over the time horizon, according to a hierarchy of arc classes. We present a mathematical model and a heuristic solution approach.     

Tabu search variants for the mix fleet vehicle routing problem

The Mix Fleet Vehicle Routing Problem (MFVRP) involves the design of a set of minimum cost routes, originating and terminating at a central depot, for a fleet of heterogeneous vehicles with various capacities, fixed costs and variable costs to service a set of customers with known demands. This paper develops new variants of a tabu search meta-heuristic for the MFVRP. These variants use a mix of different components, including reactive tabu search concepts; variable neighbourhoods, special data memory structures and hashing functions. The reactive concept is used in a new way to trigger the switch between simple moves for intensification and more complex ones for diversification of the search strategies. The special data structures are newly introduced to efficiently search the various neighbourhood spaces. The combination of data structures and strategic balance between intensification and diversification generates an efficient and robust implementation, which is very competitive with other algorithms in the literature on a set of benchmark instances for which some new best-known solutions are provided.     

Step cost functions in a fleet size and mix vehicle routing problem with time windows

Annals of Operations Research - The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several specificities...     

A Scatter Search for the periodic capacitated arc routing problem

This paper considers the Periodic Capacitated Arc Routing Problem (PCARP), a natural extension of the well-known CARP to a multi-period horizon. Its objective is to assign a set of service days to each edge in a given network and to solve the resulting CARP for each period, in order to minimize the required fleet size and the total cost of the trips on the horizon. This new and very hard problem has various applications in periodic operations on street networks, like waste collection and sweeping. A greedy heuristic and a Scatter Search (SS) are developed and evaluated on two sets of PCARP instances derived from classical CARP benchmarks. The results show that the SS strongly improves its initial solutions and clearly outperforms the greedy heuristic. Preliminary lower bounds are also provided. As they are not sufficiently tight, the SS is also tested in the single-period case (CARP) for which tight bounds are available: in fact, it competes with one state-of-the-art metaheuristic proposed for the CARP.     

A parallel insert method for the capacitated arc routing problem

The arc routing problem involves the total distance covered in traversing a certain number of arcs in a network. In the capacitated version of this problem of a finite capacity is associated with each vehicle. In this paper we introduce a new approximate solution strategy for the capacitated arc routing problem (CARP). This strategy usesd an insertion procedure to generate many routes in parallel. The purpose is to obtain a better balance between the costs of each route. Computational results are reported.     

Local search for the undirected capacitated arc routing problem with profits

This paper deals with a recently introduced routing problem variant called the undirected capacitated arc routing problem with profits (UCARPP). The UCARPP model considered in the present study is primarily aimed at generating the route set which maximizes the profit collected from a set of potential customers, represented by edges of the examined transportation network. The secondary objective is to minimize the total route travel time. The generated routes are subject both to capacity and travel time constraints. To tackle the examined problem, we propose a local search metaheuristic development which explores two solution neighborhood structures. The conducted search is effectively diversified by means of the promises concept which is based on the aspiration criteria used in tabu search approaches. The proposed algorithm was tested on UCARPP benchmark instances taken from the literature. It efficiently produced high-quality results, improving several previously best known solutions.     

Improved lower bounds and exact algorithm for the capacitated arc routing problem

In the capacitated arc routing problem (CARP), a subset of the edges of an undirected graph has to be serviced at least cost by a fleet of identical vehicles in such a way that the total demand of the edges serviced by each vehicle does not exceed its capacity. This paper describes a new lower bounding method for the CARP based on a set partitioning-like formulation of the problem with additional cuts. This method uses cut-and-column generation to solve different relaxations of the problem, and a new dynamic programming method for generating routes. An exact algorithm based on the new lower bounds was also implemented to assess their effectiveness. Computational results over a large set of classical benchmark instances show that the proposed method improves most of the best known lower bounds for the open instances, and can solve several of these for the first time.     

Two phased hybrid local search for the periodic capacitated arc routing problem

The periodic capacitated arc routing problem (PCARP) is a challenging general model with important applications. The PCARP has two hierarchical optimization objectives: a primary objective of minimizing the number of vehicles (F_v) and a secondary objective of minimizing the total cost (F_c). In this paper, we propose an effective two phased hybrid local search (HLS) algorithm for the PCARP. The first phase makes a particular effort to optimize the primary objective while the second phase seeks to further optimize both objectives by using the resulting number of vehicles of the first phase as an upper bound to prune the search space. For both phases, combined local search heuristics are devised to ensure an effective exploration of the search space. Experimental results on 63 benchmark instances demonstrate that HLS performs remarkably well both in terms of computational efficiency and solution quality. In particular, HLS discovers 44 improved best known values (new upper bounds) for the total cost objective F_c while attaining all the known optimal values regarding the objective of the number of vehicles F_v. To our knowledge, this is the first PCARP algorithm reaching such a performance. Key components of HLS are analyzed to better understand their contributions to the overall performance.     

The pyramidal capacitated vehicle routing problem

This paper introduces the pyramidal capacitated vehicle routing problem (PCVRP) as a restricted version of the capacitated vehicle routing problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the pyramidal traveling salesman problem (PTSP). A pyramidal route is defined as a route on which the vehicle first visits customers in increasing order of customer index, and on the remaining part of the route visits customers in decreasing order of customer index.     

A multi-objective capacitated rural school bus routing problem with heterogeneous fleet and mixed loads

Four multi-objective meta-heuristic algorithms are presented to solve a multi-objective capacitated rural school bus routing problem with a heterogeneous fleet and mixed loads. Three objectives are considered: the total weighted traveling time of the students, the balance of routes among drivers, and the routing costs. The proposed methods were compared with one from the literature, and their performance assessed observing three multi-objective metrics: cardinality, coverage, and hyper-volume. All four devised methods outperformed the one from the literature. The algorithm with a path relinking procedure embedded during the crowding distance selection scheme had the best overall performance.     

A variable neighborhood search for the capacitated arc routing problem with intermediate facilities

The capacitated arc routing problem (CARP) focuses on servicing edges of an undirected network graph. A wide spectrum of applications like mail delivery, waste collection or street maintenance outlines the relevance of this problem. A realistic variant of the CARP arises from the need of intermediate facilities (IFs) to load up or unload the service vehicle and from tour length restrictions. The proposed Variable Neighborhood Search (VNS) is a simple and robust solution technique which tackles the basic problem as well as its extensions. The VNS shows excellent results on four different benchmark sets. Particularly, for all 120 instances the best known solution could be found and in 71 cases a new best solution was achieved.     

Heuristic method for a mixed capacitated arc routing problem: A refuse collection application

The capacitated arc routing problem (CARP) is known to be NP-hard. The aim of this paper is to present a new heuristic method to generate feasible solutions to an extended CARP on mixed graphs, inspired by the household refuse collection problem in Lisbon. Computational experience was done to compare the method with some well-known existing heuristics, generalised for a different extended CARP by Lacomme et al. [Fast algorithm for general arc routing problems, Presented at IFORS 2002 Conference, Edinburgh, UK], namely, the Path-Scanning, the Augment-Merge and the Ulusoy’s algorithms. The results reveal a good performance of the proposed heuristic method. Generally providing a good use of the vehicles capacity, the resulting sets of feasible trips may also be considered good. The test instances involve more than 300 randomly generated test problems with dimensions of up to 400 nodes and 1220 links.     

A heuristic method for the capacitated arc routing problem with refill points and multiple loads

We describe a solution procedure for a capacitated arc routing problem with refill points and multiple loads. This problem stems from the road network marking in Quebec, Canada. Two different types of vehicles are used: the first type (called servicing vehicle—SV) with a finite capacity to service the arcs and the other (called refilling vehicle—RV) to refill the SV vehicle.The RV can deliver multiple loads, which means that it meets the SV several times before returning to the depot. The problem consists of simultaneously determining the vehicle routes that minimize the total cost of the two vehicles.We present an integer formulation and a route first-cluster second heuristic procedure. Computational results are provided.     

The mixed capacitated general routing problem under uncertainty

We study the General Routing Problem defined on a mixed graph and with stochastic demands. The problem under investigation is aimed at finding the minimum cost set of routes to satisfy a set of clients whose demand is not deterministically known. Since each vehicle has a limited capacity, the demand uncertainty occurring at some clients affects the satisfaction of the capacity constraints, that, hence, become stochastic. The contribution of this paper is twofold: firstly we present a chance-constrained integer programming formulation of the problem for which a deterministic equivalent is derived. The introduction of uncertainty into the problem poses severe computational challenges addressed by the design of a branch-and-cut algorithm, for the exact solution of limited size instances, and of a heuristic solution approach exploring promising parts of the search space. The effectiveness of the solution approaches is shown on a probabilistically constrained version of the benchmark instances proposed in the literature for the mixed capacitated general routing problem.     

The capacitated general windy routing problem with turn penalties

In this paper we present the capacitated general windy routing problem with turn penalties. This new problem subsumes many important and well-known arc and node routing problems, and it takes into account turn penalties and forbidden turns, which are crucial in many real-life applications, particularly in downtown areas and for large vehicles. We provide a way to solve this problem both optimally and heuristically by transforming it into a generalized vehicle routing problem.     

A survey on maritime fleet size and mix problems

This paper presents a literature survey on the fleet size and mix problem in maritime transportation. Fluctuations in the shipping market and frequent mismatches between fleet capacities and demands highlight the relevance of the problem and call for more accurate decision support. After analyzing the available scientific literature on the problem and its variants and extensions, we summarize the state of the art and highlight the main contributions of past research. Furthermore, by identifying important real life aspects of the problem which past research has failed to capture, we uncover the main areas where more research will be needed.