Open Vehicle Routing Problem Research Articles

OVRP_GELS: solving open vehicle routing problem using the gravitational emulation local search algorithm

In open vehicle routing problem (OVRP), after delivering service to the last customer, the vehicle does not necessarily return to the initial depot. This type of problem originally defined about thirty years ago and still is an open issue. In real life, the OVRP is similar to the delivering newspapers and consignments. The problem of service delivering to a set of customers is a particular open VRP with an identical fleet for transporting vehicles that do not necessarily return to the initial depot. Contractors which are not the employee of the delivery company use their own vehicles and do not return to the depot. Solving the OVRP means to optimize the number of vehicles, the traveling distance and the traveling time of a vehicle. In time, several algorithms such as tabu search, deterministic annealing and neighborhood search were used for solving the OVRP. In this paper, a new combinatorial algorithm named OVRP_GELS based on gravitational emulation local search algorithm for solving the OVRP is proposed. We also used record-to-record algorithm to improve the results of the GELS. Several numerical experiments show a good performance of the proposed method for solving the OVRP when compared with existing techniques.

Open vehicle routing problem with cross-docking

The advantages of the cross-docking technique have been increasingly appreciated in literature and in practice. This appreciation, coupled with the advances of numerous applications in the vehicle routing problem (VRP) across numerous practical contexts, presents an opportunity to explore the open VRP with cross-docking (OVRPCD). We introduce a general example in retail wherein the capital expenditure necessary in vehicle acquisition can become a burden for the retailer, who then needs to consider outsourcing a logistics service as a cost-effective option. This practical scenario can be applied to create an open flow network of routes. This study considers a single product and single cross-dock wherein capacitated homogeneous vehicles start at different pickup points and times during pickup operations. The vehicles are scheduled to route in the network synchronously to arrive at the cross-dock center simultaneously. In the delivery operations, all customers must be served at most once and deliveries should be finished within a predetermined duration. We model OVRPCD as a mixed-integer linear program that minimizes the total cost (vehicle hiring cost and transportation cost). A simulated annealing (SA) algorithm is proposed to solve the problem. SA is first verified by solving benchmark instances for the vehicle routing problem with cross-docking and comparing the results with those obtained by existing ​state-of-art algorithms. We then test SA on three sets of OVRPCD benchmark instances and the results are compared with those obtained by CPLEX. Computational results show that both CPLEX and SA can obtain optimal solutions to all small and medium instances. However, the computational time required by SA is shorter than that needed by CPLEX. Moreover, for large instances, SA outperforms CPLEX in both solution value and computational time.

A Modified Column Generation to Solve the Heterogeneous Fixed Fleet Open Vehicle Routing Problem

In the heterogeneous fixed fleet open vehicle routing problem (HFFOVRP), several different types of vehicles can be used to service the customers. The types of vehicles are different in terms of capacity, fixed cost, and variable cost. In this problem, the vehicles are not required to return to the depot after completing a service and the number of vehicles of each type is fixed and limited. Since this problem belongs to NP-hard problems, in this paper a compound heuristic algorithm called SISEC which includes sweep algorithm, insert, swap, and 2-opt moves, modified elite ant system (EAS), and column generation (CG) is applied to solve the HFFOVRP. We report computational results on 22 problems and solve each problem by using our SISEC. The results which were compared to the results of exact algorithms and the classic CG confirm that the proposed algorithm produces high quality solutions within an acceptable computation time.

An improved formulation for the multi-depot open vehicle routing problem

The multi-depot open vehicle routing problem (MDOVRP) is a recent hard combinatorial optimization problem that belongs to the vehicle routing problem family. In the MDOVRP, the vehicles depart from several depots and once they have delivered the goods to the last customers in their routes they are not required to return to the depots. In this work, we propose a new mixed integer programming formulation for the MDOVRP by improving some constraints from the literature and proposing new ones. The computational experience carried out over problem instances from the literature indicates that our proposed model outperforms the existing one.

EDAL: An Energy-Efficient, Delay-Aware, and Lifetime-Balancing Data Collection Protocol for Heterogeneous Wireless Sensor Networks

Our work in this paper stems from our insight that recent research efforts on open vehicle routing (OVR) problems, an active area in operations research, are based on similar assumptions and constraints compared to sensor networks. Therefore, it may be feasible that we could adapt these techniques in such a way that they will provide valuable solutions to certain tricky problems in the wireless sensor network (WSN) domain. To demonstrate that this approach is feasible, we develop one data collection protocol called EDAL, which stands for Energy-efficient Delay-aware Lifetime-balancing data collection. The algorithm design of EDAL leverages one result from OVR to prove that the problem formulation is inherently NP-hard. Therefore, we proposed both a centralized heuristic to reduce its computational overhead and a distributed heuristic to make the algorithm scalable for large-scale network operations. We also develop EDAL to be closely integrated with compressive sensing, an emerging technique that promises considerable reduction in total traffic cost for collecting sensor readings under loose delay bounds. Finally, we systematically evaluate EDAL to compare its performance to related protocols in both simulations and a hardware testbed.

An ACO hybrid metaheuristic for close–open vehicle routing problems with time windows and fuzzy constraints

The close–open vehicle routing problem is a realistic variant of the “classical” vehicle routing problem where the routes can be opened and closed, i.e. all the vehicles are not required to return to the depot after completing their service. This variant is a planning model that is a standard practice in business nowadays. Companies are contracting their deliveries to other companies that hire vehicles, and payment is made based on the distance covered by the vehicles. Available information on parameters in real world situations is also imprecise, and must be included in the optimization model and method. The aims of this paper are to formulate a model of this novel variant with time windows and imprecise constraints and to propose a fuzzy optimization approach and a hybrid metaheuristic for its solutions. The full proposal is applied to a real route planning problem with outsourcing, obtaining promising practical results. Customer demands and travel times are imprecise, thus capacity and time windows constraints are considered flexible and modelled as fuzzy constraints.

The offshore wind farm array cable layout problem: a planar open vehicle routing problem

In an offshore wind farm (OWF), the turbines are connected to a transformer by cable routes that cannot cross each other. Finding the minimum cost array cable layout thus amounts to a vehicle routing problem with the additional constraints that the routes must be embedded in the plane. For this problem, both exact and heuristic methods are of interest. We optimize cable layouts for real-world OWFs by a hop-indexed integer programming formulation, and develop a heuristic for computing layouts based on the Clarke and Wright savings heuristic for vehicle routing. Our heuristic computes layouts on average only 2% more expensive than the optimal layout. Finally, we present two problem extensions arising from real-world OWF cable layouts, and adapt the integer programming formulation to one of them. The thus obtained optimal layouts are up to 13% cheaper than the actually installed layouts.

A new approach to open vehicle routing problem with time window considering vehicle age and monetary value

There has been a great deal of recent interest in considering different cost component and economic issues in transportation and routing models to achieve robust results. The major issues in economics of transportation and routing problems are monetary value, benefits, costs, inflation, depreciation, and different taxes. In this paper all usage cost components are considered in the proposed open vehicle routing problem with time windows (OVRPTW) model, monetary value of all costs and also age of vehicles and its influence on each cost component are analysed. Based on this research a more robust calculation of the model, both for owned and rented vehicles and the integration of both are obtained and also it is concluded the number of vehicles and travelled distance are not drastically affected by the age of vehicles. Moreover, the number of vehicles and routes are constructed based on optimal age of vehicles, full cost and monetary value.

Response and recovery after severe wind storms using hierarchical open vehicle routing

This research represents a novel application of operations research methodology to a form of a hierarchical open vehicle routing problem. In our case study, a road network was divided into priority sets such that each set needed to be completely addressed before work could begin on the next. Rule-based heuristics and adaptations of local beam search heuristics were tested in various combinations, viable solutions were developed, and results were evaluated based on the time required to clear the entire road network of storm-generated debris. The results were also compared against a theoretical lower bound on the time required to clear all roads. The best routes were generated using a combination of constant time beam search and a rule-based heuristic, 12.4% greater than the lower bound, yet understandable for the case study area that contained numerous dead-ends and disconnected road priority sets.

Research of Oil Product Secondary Distribution Optimization Based on Collaborative Distribution

Abstract During peak seasons, the petrol company's oil supply capacity is insufficient, therefore, with limited trucks, adjusting the distribution quantity of petrol station and formulating an effective distribution route can minimize the total cost and maximize the vehicle utilization. In this paper we observe the extension of the multi-depot half open vehicle routing problem with time windows (MDHOVRPTW) in oil product secondary distribution. Based on the characteristics of secondary distribution and MDHOVRPTW problem, this paper formulates oil distribution model intra-area with distribution quantity and distribution routing as decision variables. A proposed algorithm is applied to solve this model and result compared with the traditional non-cooperative method to verify the effectiveness of collaborative distribution.

Applying Tabu Search in Finding an Efficient Solution for the OVRP

In the open vehicle routing problem (OVRP), the target would be to reduce the amount of vehicles after reducing the whole distance (or time) travelled. Every route begins at the depot and comes to an end at a customer, going to many customers, every once, en route, without returning to the depot. The demand of every customer has to be completely fullled by a single vehicle. The total demand serviced by each vehicle has to not go over vehicle capacity. A highly eective tabu search for open vehicle routing called Three Strategies Tabu Search (TSTS) heuristic for this problem is suggested. The TSTS depends on three strategies MOVE, EXCHANGE and SWAP. Computational results on fourteen standard benchmark problem instances demonstrate that the suggested TSTS is comparable in terms of solution quality for the best performing published heuristics.

A multi-start algorithm for a balanced real-world Open Vehicle Routing Problem

The aim of this paper is to solve a real-world problem proposed by an international company operating in Spain and modeled as a variant of the Open Vehicle Routing Problem in which the makespan, i.e., the maximum time spent on the vehicle by one person, must be minimized. A competitive multi-start algorithm, able to obtain high quality solutions within reasonable computing time is proposed. The effectiveness of the algorithm is analyzed through computational testing on a set of 19 school-bus routing benchmark problems from the literature, and on 9 hard real-world problem instances.

Open Vehicle Routing Problem by Ant Colony Optimization

Vehicle routing problem (VRP) is real-world combinatorial optimization problem which determine the optimal route of a vehicle. Generally, toprovide the efficientvehicle serving to the customer through different services by visiting the number of cities or stops. The VRP follows the Travelling Salesman Problem (TSP), in which each of vehicle visiting a set of cities such that every city is visited by exactly one vehicle only once. This work proposes the Ant Colony Optimization (ACO)-TSP algorithm to eliminate the tour loop for Open Vehicle routing Problem (OVRP). A key aspect of this algorithm is to plan the routes of buses that must pick up and deliver the school students from various bus stops on time, especially in the case of far distance covered by the vehicle in a rural area and find out the efficient and safe vehicle route.

A Survey of Transportation Problems

This paper aims at being a guide to understand the different types of transportation problems by presenting a survey of mathematical models and algorithms used to solve different types of transportation modes (ship, plane, train, bus, truck, Motorcycle, Cars, and others) by air, water, space, cables, tubes, and road. Some problems are as follows: bus scheduling problem, delivery problem, combining truck trip problem, open vehicle routing problem, helicopter routing problem, truck loading problem, truck dispatching problem, truck routing problem, truck transportation problem, vehicle routing problem and variants, convoy routing problem, railroad blocking problem (RBP), inventory routing problem (IRP), air traffic flow management problem (TFMP), cash transportation vehicle routing problem, and so forth.

A Bumble Bees Mating Optimization algorithm for the Open Vehicle Routing Problem

Bumble Bees Mating Optimization (BBMO) algorithm is a relatively new swarm intelligence algorithm that simulates the mating behaviour that a swarm of bumble bees performs. In this paper, an improved version of the BBMO algorithm is presented for successfully solving the Open Vehicle Routing Problem. The main contribution of the paper is that the equation which describes the movement of the drones outside the hive has been replaced by a local search procedure. Thus, the algorithm became more suitable for combinatorial optimization problems. The Open Vehicle Routing Problem (OVRP) is a variant of the classic vehicle routing problem. In the OVRP the vehicles do not return to the depot after the service of the customers. Two sets of benchmark instances were used in order to test the proposed algorithm. The obtained results were very satisfactory as in most instances the proposed algorithm found the best known solutions. More specifically, in the fourteen instances proposed by Christofides, the average quality was 0.09% when a hierarchical objective function was used, where, first, the number of vehicles is minimized and, afterwards, the total travel distance is minimized and the average quality was 0.11% when only the travel distance was minimized while for the eight instances proposed by Li et al. when a hierarchical objective function was used the average quality was 0.06%. The algorithm was, also, compared with a number of metaheuristic, evolutionary and nature inspired algorithms from the literature.

Variable neighbourhood search for close–open vehicle routing problem with time windows

Variable neighbourhood search for close–open vehicle routing problem with time windows

Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm

The vehicle routing problem (VRP) is a well-known combinatorial optimisation problem and holds a central place in logistics management. Many exact, heuristic and metaheuristic approaches have been proposed to solve VRP. An important variant of the VRP arises when a fleet of vehicles is fixed and characterised by different capacities for distribution activities. The problem is known as the heterogeneous fixed fleet VRP (HFFVRP). The HFFVRP is a natural generalisation of the VRP with several vehicle types, each type being defined by a capacity, a fixed cost and a cost per distance unit, and can cover more practical situations in transportation. This problem consists of determining a set of vehicle trips of minimum total length in which a set of customers is to be satisfied in the demand constraints using identical vehicles with limited capacity. If open routes instead of closed ones are considered in the HFFVRP, the problem becomes a heterogeneous fixed fleet Open VRP (HFFOVRP) which has numerous applications in industrial and service problems. In this paper, a bone route algorithm which uses the tabu search as an improved procedure is utilised to solve the HFFOVRP. The proposed algorithm was tested empirically on a 24 of generated VRPs, and compared with elite ant system and ant colony system. In all cases, the proposed algorithm finds the best-known solutions within a reasonable time.

Open vehicle routing problem with demand uncertainty and its robust strategies

We investigate the open vehicle routing problem with uncertain demands, where the vehicles do not necessarily return to their original locations after delivering goods to customers. We firstly describe the customer’s demand as specific bounded uncertainty sets with expected demand value and nominal value, and propose the robust optimization model that aim at minimizing transportation costs and unsatisfied demands in the specific bounded uncertainty sets. We propose four robust strategies to cope with the uncertain demand and an improved differential evolution algorithm (IDE) to solve the robust optimization model. Then we analyze the performance of four different robust strategies by considering the extra costs and unmet demand. Finally, the computational experiments indicate that the robust optimization greatly avoid unmet demand while incurring a small extra cost and the optimal return strategy is the best strategy by balancing the trade-off the cost and unmet demand among different robust strategies.

Erratum to: A hybrid genetic algorithm for the multi-depot open vehicle routing problem

Erratum to: A hybrid genetic algorithm for the multi-depot open vehicle routing problem

Study on a Multi-Depot and Heterogeneous-Vehicle Open Vehicle Routing Problem to Reduce Fuel Consumption

An open vehicle routing problem is studied. In this problem, multi-depot, heterogeneous-vehicle, fuel consumption and start-up costs of vehicles are considered, thus a genetic algorithm is given to solve this hard problem. In order to improve the performance of the genetic algorithm, a heuristic algorithm is provided to produce the initial population and participate in crossover. An example is given to illustrate the genetic algorithm.