As the number and severity of snowfall events continue to grow, the need to direct road maintenance intelligently during these snowfall events will also grow. In several locations, local governments lack the resources to treat all roadways completely during snow events. Furthermore, some governments utilize only traffic data to determine which roads should be treated. As a result, many schools, businesses, and government offices must be unnecessarily closed, which directly impacts the social, educational, and economic well-being of citizens and institutions. In this work, we propose a mixed integer programming (MIP) formulation to allocate resources to manage snowfall on roads using meteorological, geographical, and environmental parameters. Given that MIPs often scale poorly with problem size, we also present a constructive heuristic designed for the problem. Additionally, we evaluate the impacts of an increase in budget for winter road maintenance on snow control resources.
The VeRoLog Solver Challenge 2019 is the $${4{\mathrm{th}}}$$ solver challenge facilitated by VeRoLog, the EURO Working Group on Vehicle Routing and Logistics. The challenge is organized in cooperation with ORTEC. On behalf of the organizing committee, the authors report on the problem and organization of the challenge.
In the European Union, truck drivers must comply with Regulation (EC) No 561/2006, which provides a set of rules on the daily or weekly working time and on break or rest periods after specific working times. Truck drivers can be back to the depot much earlier than the end of their working period, and be able to perform other trips. The resulting problem is a Multi-Trip Vehicle Routing Problem with Time Windows, where truck drivers have the possibility to accomplish, during their time horizon, more than one trip, combined with a Truck Driver Scheduling Problem. It aimed to find and assign a set of routes to a fleet of vehicles allowing each customer to be visited within its given time window, and the accumulated load to be delivered (or collected) not exceeding the capacity of the vehicle. Each truck driver must comply with applicable hours of service regulations, and the objective is to minimize total transportation cost. To solve this problem, we have developed a hybrid method composed of a genetic algorithm and a local neighborhood search. Experiments have been conducted on instances from the literature and real-life cases from SYSTRANS, a specialized French software company.
In this paper, we develop an intelligent solution to a complex, real-life vehicle routing problem in the waste management sector. Waste management companies deliver various types of empty waste containers to industrial customers, to be filled with different types of waste, after which the containers are picked up again. The full containers are transported to a so-called waste management depot or waste handling depot, where they are emptied, after which they are reused. Empty containers are stocked in various stock depots. Time windows in which containers may be picked up and delivered at the customers and opening hours of the different depots have to be taken into account additionally. Very importantly, there are two types of waste collection trucks that can, respectively, carry one or two containers. The resulting vehicle routing problem belongs to a class of so-called roll-on–roll-off problems, characterized by unit demand. Additionally, the problem discussed in this paper has several characteristics (multiple waste types, multiple container types, multiple depots, a heterogeneous fleet, pickup and delivery, time window constraints, and other) that make solving it a difficult task. To solve this problem, we develop a novel column generation scheme that incorporates a heuristic approach to generate new columns. The master problem is solved by linear relaxation of a set partitioning problem. New routes (columns) are generated by a constructive heuristic loosely based on Solomon’s insertion heuristic for the vehicle routing problem with time windows. The construction heuristic operates on a reformulated version of the roll-on–roll-off problem, i.e., a generalized vehicle routing problem with time windows. The algorithm—called wmpopt—is submitted to an extensive sensitivity analysis to determine its response to different parameter settings. After this, we test it on four real-life problem instances and compare its results to those obtained by a commercial solver. We show that wmpopt achieves much better solutions than the commercial solver in similar computing times.
This paper addresses the dial-a-ride problem (DARP) using private vehicles and alternative nodes (DARP-PV-AN). The DARP consists of creating vehicle routes in order to ensure a set of users’ transportation requests. Each request corresponds to a client needing to be transported from his/her origin to his/her destination. Routing costs have to be minimized while respecting a set of constraints like time windows and maximum route length. In the classical DARP, vehicles have to start from a depot and come back to it at the end of their route. In the DARP-PV-AN, the on-demand transportation service can be done either by a public fleet or by clients that use their private vehicles. The use of these vehicles adds more flexibility and unclog the public transportation fleet by allowing clients to organize their own transportation. However, it also raises some privacy concerns. The DARP-PV-AN addresses these concerns and focuses on location privacy, i.e., the ability to prevent the third parties from learning clients’ locations, by keeping both original and final locations private. This is addressed by setting several pickup/delivery nodes for the transportation requests, thus masking the private address. A compact mixed integer linear model is presented, and an evolutionary local search (ELS) is proposed to compute solutions of good quality for the problem. These methods are benchmarked on a modified set of benchmark instances. A new set of realistic instances is also provided to test the ELS in a more realistic way.
A metropolitan area experiences transport resource scarcities and dynamic resource allocation problems due to huge number of commuters’ population, dynamic commuters’ arrival rates, etc. The progress of these problems results into economic loss, traffic congestion, inefficient utilization of resources and increase in indefinite waiting time of commuters. Hence, we propose a dynamic transport resource allocation scheme. The scheme efficiently manages number of vehicles over time and space using emergent intelligence (EI) technique. Based on the historical information, commuters’ arrival rates, resource availability, deficit resources, surplus resources of neighbor depots, etc., the EI technique with agents is used for collecting, analyzing, sharing and allocating resources, for optimal utilization of resources in a metropolitan area. Analytical model of EI technique-based transport resource allocation scheme is developed using Markov chain, and derived the closed-form expression of optimal utilization of resources. Performance evaluation is carried out with varying number of commuters’ arrival rates, vehicles, requests and number of neighborhood depots. We observe that results obtained in the simulation and analysis reflect the effectiveness of the proposed scheme in a metropolitan area.
Many of the algorithms for solving vehicle routing problems expose parameters that strongly influence the quality of obtained solutions and the performance of the algorithm.Finding good values for these parameters is a tedious task that requires experimentation and experience. Therefore, methods that automate the process of algorithm configuration have received growing attention. In this paper, we present a comprehensive study to critically evaluate and compare the capabilities and suitability of seven state-of-the-art methods in configuring vehicle routing metaheuristics. The configuration target is the solution quality of eight metaheuristics solving two vehicle routing problem variants. We show that the automatic algorithm configuration methods find good parameters for the vehicle route optimization metaheuristics and clearly improve the solutions obtained over default parameters. Our comparison shows that despite some observable differences in configured performance there is no single configuration method that always outperforms the others. However, largest gains in performance can be made by carefully selecting the right configurator. The findings of this paper may give insights on how to effectively choose and extend automatic parameter configuration methods and how to use them to improve vehicle routing solver performance.
The VeRoLog Solver Challenge 2016–2017 is the third solver challenge facilitated by VeRoLog, the EURO Working Group on Vehicle Routing and Logistics Optimization, and is organized in cooperation with ORTEC B.V. The authors constitute the organizing committee of this challenge, and with this paper they report on the problem and organization of this challenge.
This paper is concerned with the problem of the characteristic function evaluation for the game theory model of horizontal cooperation of carriers on large transportation networks. We consider a mathematical formalization of the Cooperative Inventory Routing Game (CIRG) in the form of characteristic function. Due to non-exact evaluation of the minimal cost for the coalitions, we have the subadditivity property of the characteristic function to be not fulfilled in general case. To calculate the values of characteristic function that satisfy the subadditivity condition, the Direct Coalition Induction Algorithm (DCIA) is used. To solve the multi-depot Inventory Routing Problem for each coalition, the Dynamic Adaptation procedure for Large Neighborhood Search (ALNS) is applied. Calculation of the characteristic function vales, DCIA performance, and advantages of Dynamic Adaptation for ALNS are demonstrated with computational experiments. It is shown that an experimental level of time consistency of the solutions generated by DALNS for given IRP benchmark instances appears to be higher in average in comparison with the solutions generated by ALNS.
In the classical (Capacitated) Vehicle Routing Problem (CVRP) we seek to use a fleet of trucks to deliver goods to customers at minimal cost, and customers’ requests must be fulfilled in a single visit. In the Split Delivery Vehicle Routing Problem (SDVRP), we are allowed to visit a customer multiple times to fulfil their demand. In this paper, we study a variant of SDVRP where customers have to be served over a multi-period horizon, and each customer may require service on one or more days. We consider the possibility of splitting a request not only between vehicles on the same day but also across consecutive days. The objective is to find a set of routes for each day of the planning horizon so that the total travelling cost is minimised, and the total amount delivered meets customers’ demand. We show that this Multi-Day version of SDVRP is structurally different to the usual SDVRP. We also consider a Fleet Size and Mix variant of the problem, where a fixed cost for using a vehicle at all during the horizon is added to the objective function. We propose a Mixed Integer Linear Programming approach to solve the Multi-Day SDVRP, together with some valid inequalities to enhance it. Furthermore, we develop a large neighbourhood search-based heuristic which provides upper bounds for the proposed mathematical formulation, which proves effective in reducing solution times. We present a theoretical study of the problem, extending some known properties of the VRP with split deliveries, and an extensive computational analysis aimed at studying the strengths and weakness of the proposed strategy.
Intelligent navigation in cluttered environment while insuring maximum safety and task efficiency is a challenging subject. Motion planning is an important issue in the field of autonomous mobile robots which makes them capable to travel from one position to another in various environments including both static and dynamic obstacles without any human intervention. This research is conducted for the purpose of designing and programming a mobile robot using two separated fuzzy logic controllers to develop an intelligent algorithm in order to avoid both static and dynamic obstacles. These fuzzy logic controllers play a significant role in mobile robot navigation and obstacle avoidance behavior. In this work, four essential behavior controllers are designed and implemented onto the robot to assist its navigation towards the goal which are: goal reaching behavior, speed control behavior, goal searching behavior and obstacle avoidance behavior. The obstacle avoidance behavior is divided into two individual behaviors which are static obstacle avoidance behavior and dynamic obstacle avoidance behavior where these behaviors are controlled by an artificial intelligence (AI) algorithm. In order to design obstacle avoidance behavior, Sugeno fuzzy logic was applied. The simulation of this research was done by MATLAB software where a mobile robot and some experimental environments with different complexity were created. Several navigation tests were conducted and the robot’s behavior were observed as well. Analysis of the robot’s performance validated the effectiveness of the proposed controllers and the robot could successfully navigate to reach the goal through all experimental environments.
In this paper, we study the vehicle routing problem with dynamic customers, where a portion of the customer requests are known in advance and the rest arrive in real time. We propose an optimization-based look-ahead dynamic routing framework that involves request forecasting, partial planning, and dynamic real-time routing of the fleet. This framework has the capabilities for adjustments in response to routing environments with different levels of uncertainties. Through extensive numeral simulations, we exam its performance in routing environments with various levels of uncertainties. We demonstrate the efficiency and robustness of the proposed solution by benchmarking against two other routing strategies. This paper fills the gap in the literature on studying the relationship between the level of route planning in the solution approach and the quality of the solution under various system conditions.
We consider a dynamic vehicle routing problem with mixed backhauls (DVRPMB) that seeks to plan, in the most efficient way, the delivery of dynamic pickup orders that arrive in real time, while a predefined plan of serving static delivery orders is being executed. Maintaining the original assignment of delivery orders to vehicles may limit system performance, since the changes in the system state caused by the arriving dynamic orders may grant re-assignments of such orders advantageous. Thus, in this paper, we introduce and solve a variant of DVRPMB that allows orders to be transferred between vehicles during plan implementation. We refer to this problem as the DVRPMB with load transfers (DVRPMB-LT). Since the problem is solved with periodic re-optimization, we focus on the underlying optimization problem, develop an appropriate model using an arc-based formulation, and compare the exact solutions to the ones of the corresponding problem that does not allow transfers. Furthermore, we develop a practical heuristic framework to address the complexity of DVRPMB-LT and solve cases of practical relevance. Subsequently, we employ the proposed framework to solve and analyze the full dynamic problem.
A metropolitan area is an area with dynamic demands and is one of the main indicators of economic growth of nation. It involves the complexity of efficient analysis and prediction of patterns of growth or decline of traffic volume and patterns of resource utilization with respect to time and place. To solve these complexities, we propose agent-based commuters’ traffic pattern and prediction analysis model in a metropolitan area. The proposed system model is capable of analyzing and predicting the patterns of commuters’ traffic flow volume and resource utilization in each zone and region, using the population density, availability of resources, type of place, time period, and commuters’ and vehicles’ arrival rates. The proposed model provides qualitative form of traffic; increases the probability of measure of unpredictable information; and aids in emergency traffic planning and route-finding services. The result shows the effectiveness of the model at different time periods in a day for forecasting of the resource utilization and changes in traffic volumes in zones and regions in the metropolitan area.
Synchronisation in vehicle routing is a rather new field of research and naturally new problems arise. One of these problems is the Line-haul Feeder Vehicle Routing Problem (LFVRP). It uses a fleet of small and large vehicles to serve two types of customers. The first type provides additional parking space and can be visited by both vehicle classes. The second type can only be visited by the small vehicle class as these customers provide only limited parking space. The main characteristic of the small vehicle class is the limited capacity. To overcome this particular disadvantage, the small vehicles can use the large vehicles as virtual depots. In other words, a small and large vehicle can meet at a parking lot or at a customer with enough space (type-1 customer) and perform a transfer of goods. For a successful reloading operation, both vehicles must be present at the same place at the same time. Thus, both vehicle tours must be synchronized. After using the large vehicle as virtual depot, the small vehicle can proceed immediately afterwards because it does not need to go back to the physical depot. Consequently, less time and distance is required which results in a reduction of the overall costs. The advantage of the LFVRP over classical variants of the Vehicle Routing Problem has been shown in previous papers. Yet, customer time windows have been neglected so far and as time windows play an important role in vehicle routing research, they need to be addressed properly. Therefore, we aim to close this gap by introducing the Line-haul Feeder Vehicle Routing Problem with Time Windows (LFVRPTW). We discuss the complexity of customer time windows for the LFVRPTW and adopt the previously introduced algorithm for the LFVRP. Furthermore, we provide a thorough computational analysis on the impact of different time window characteristics and show the advantage of the LFVRPTW over other variants of the Vehicle Routing Problem with Time Windows.
We describe a weighted version of the k-Chinese and k-rural postman problem that occurs in the context of snow removal. The problem concerns the questions of which vehicle shall take care of each link and how the vehicles shall travel between links. We also consider different numbers of vehicles, in view of a fixed cost for each vehicle. We describe and discuss heuristic solution approaches, based on usable substructures, such as heuristics for rural postman problems, meta-heuristics, k-means clustering and local search improvements by moving cycles. The methods have been implemented and tested on real life examples.
