We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates transportation services for a limited number of partners and should respect contractual obligations on service levels. The problem also generalizes several important classes of vehicle routing problems with profits. To solve it, we propose a compact mathematical formulation, a branch-and-price algorithm, and a hybrid genetic algorithm with population management, which relies on problem-tailored solution representation, crossover and local search operators, as well as an adaptive penalization mechanism establishing a good balance between service levels and costs. Our computational experiments show that the proposed heuristic returns very high-quality solutions for this difficult problem, matches all optimal solutions found for small and medium-scale benchmark instances, and improves upon existing algorithms for two important special cases: the vehicle routing problem with private fleet and common carrier, and the capacitated profitable tour problem. The branch-and-price algorithm also produces new optimal solutions for all three problems.
This paper introduces the two-level capacitated vehicle routing problem (2S-CVRP). This problem combines the two-level bin packing problem and the vehicle routing problem into an integrated framework. The problem itself is an NP-hard problem and it can be seen as an extension to the traditional capacitated vehicle routing problem (CVRP). We propose this extension as it enable one to model more real-life applications in logistics. A mixed integer program (MIP) model is presented for the problem. Our MIP model includes an extensive set of constraints encountered in real-world applications. The v…
The multi Vehicle Routing Problem with Pickup and Delivery with Time Windows is a challenging version of the Vehicle Routing Problem. In this paper, by embedding many complex assignment routing constraints through constructing a multi dimensional network, we intend to reach optimality for local clusters derived from a reasonably large set of passengers on real world transportation networks. More specifically, we introduce a multi vehicle state space time network representation in which only the non dominated assignment based hyper paths are examined. In addition, by the aid of passengers cumul…
After the April 2015 Nepal Earthquake, the Himalayan Disaster Relief Volunteer Group distributed supplies to affected areas. We model HDRVG's operations as a vehicle routing problem using Fisher and Jaikumar's two stage method, which allocates locations to vehicles via an integer program and then uses heuristics to route the vehicles. In the allocation stage, we use the assignment problem formulation to assign locations to vehicles. In the routing stage, we implement multiple heuristics for the sake of comparison. Our results illustrate the open nature of the vehicle routing problem and the co…
Green vehicle routing problem (GVRP) aims to consider greenhouse gas emissions reduction, while routing the vehicles. It can be either through adopting Alternative Fuel Vehicles (AFVs) or with existing conventional fossil fuel vehicles in fleets. GVRP also takes into account environmental sustainability in transportation and logistics. We critically review several variations and specializations of GVRP to address issues related to charging, pickup, delivery, and energy consumption. Starting with the concepts and definitions of GVRP, we summarize the key elements and contributors to GVRP public…
Energy consumption is the major contributor associated with large and growing transportation cost in logistics. Optimal vehicle routing approaches can provide solutions to reduce their operating costs and address implications on energy. This paper outlines a solution to the single-depot capacitated vehicle routing problem with the objective of minimizing daily operation cost with a homogeneous fleet of delivery vehicles. The problem is solved using Simulated Annealing, to provide optimal routes for the vehicles traveling between the depot and destinations. Simulation results demonstrate that t…
An equitable distribution of workload is essential when deploying vehicle routing solutions in practice. For this reason, previous studies have formulated vehicle routing problems with workload-balance objectives or constraints, leading to trade-off solutions between routing costs and workload equity. These methods consider a single planning period; however, equity is often sought over several days in practice. In this work, we show that workload equity over multiple periods can be achieved without impact on transportation costs when the planning horizon is sufficiently large. To achieve this,…
This article considers a cooperative vehicle routing problem for an intelligence, surveillance, and reconnaissance mission in the presence of communication constraints between the vehicles. The proposed framework uses a ground vehicle and an Unmanned Aerial Vehicle (UAV) that travel cooperatively and visit a set of targets while satisfying the communication constraints. The problem is formulated as a mixed-integer linear program, and a branch-and-cut algorithm is developed to solve the problem to optimality. Furthermore, a transformation method and a heuristic are also developed for the proble…
Electric vehicle routing problems can be particularly complex when recharging must be performed mid-route. In some applications such as the e-commerce parcel delivery truck routing, however, mid-route recharging may not be necessary because of constraints on vehicle capacities and maximum allowed time for delivery. In this study, we develop a mixed-integer optimization model that exactly solves such a time-constrained capacitated vehicle routing problem, especially of interest to e-commerce parcel delivery vehicles. We compare our solution method with an existing metaheuristic and carry out ex…
We study the problem of routing vehicles with energy constraints through a network where there are at least some charging nodes. We seek to minimize the total elapsed time for vehicles to reach their destinations by determining routes as well as recharging amounts when the vehicles do not have adequate energy for the entire journey. For a single vehicle, we formulate a mixed-integer nonlinear programming (MINLP) problem and derive properties of the optimal solution allowing it to be decomposed into two simpler problems. For a multi-vehicle problem, where traffic congestion effects are included…
The Heterogeneous Fleet Vehicle Routing Problem (HFVRP) is an important variant of the classical Capacitated Vehicle Routing Problem (CVRP) that aims to find routes that minimize the total traveling cost of a heterogeneous fleet of vehicles. This problem is of great interest given its importance in many industrial and commercial applications. In this paper, we present an Adaptive Iterated Local Search (AILS) heuristic for the HFVRP. AILS is a local search-based meta-heuristic that achieved good results for the CVRP. The main characteristic of AILS is its adaptive behavior that allows the adjus…
We study the problem of eco-routing Plug-In Hybrid Electric Vehicles (PHEVs) to minimize the overall energy consumption costs. Unlike the traditional Charge Depleting First (CDF) approaches in the literature where the power-train control strategy is fixed, we propose a Combined Routing and Power-train Control (CRPTC) algorithm which can simultaneously calculate the optimal energy route as well as the optimal power-train control strategy. To validate our method, we apply our eco-routing algorithm to a subnetwork of the Eastern Massachusetts (EMA) transportation network using actual traffic data…
We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We study two versions of the problem. In the single vehicle routing problem, we formulate a mixed-integer nonlinear programming (MINLP) problem and show that it can be reduced to a lower dim…
The Vehicle Routing Problem with Route Balancing (VRPRB) is a biobjective version of the original Vehicle Routing Problem (VRP) in which, besides minimizing the total distance traveled by the vehicles involved, the balance among route loads is also pursued. Different objective functions (OFs) to achieve balanced route configurations have been proposed in the literature, however to the best of the authors knowledge there is still no consensus on which OF is the most suitable one for addressing, through metaheuristics, this challenging multiobjective optimization problem. This paper inquires int…
We study a new variant of the vehicle routing problem, called the Mobile Production Vehicle Routing Problem (MoP-VRP). In this problem, vehicles are equipped with 3D printers, and production takes place on the way to the customer. The objective is to minimize the weighted cost incurred by travel and delay of service. We formulate a Mixed Integer Programming (MIP) model and develop an Adaptive Large Neighbourhood Search (ALNS) heuristic for this problem. To show the advantage of mobile production, we compare the problem with the Central Production Vehicle Routing Problem (CP-VRP), where product…
This work considers the problem of optimize the routes of the vehicles used by a real agricultural cooperative that distributes animal feed among the partners. Because solving the exact model is computationally burdensome, we propose to implement heuristic algorithms. Thus, firstly an initial solution is obtained through an insertion heuristic algorithm. Secondly, we design a simulated annealing algorithm for possible improvements on the initial solution. Finally, we built a graphical interface to quickly and easily interact with the system.
Managing all the mobility and transportation services with autonomous vehicles for users of a smart city requires determining the assignment of the vehicles to the users and their routing in conjunction with their speed. Such decisions must ensure low emission, efficiency, and high service quality by also considering the impact on traffic congestion caused by other vehicles in the transportation network. In this paper, we first propose an abstract trilevel multi-objective formulation architecture to model all vehicle routing problems with assignment, routing, and speed decision variables and c…
In this short paper, we study the capacity-constrained vehicle routing problem (CVRP) and its solution by randomized Monte Carlo methods. For solving CVRP we use some pseudorandom number generators commonly used in practice. We use linear, multiple-recursive, inversive, and explicit inversive congruential generators and obtain random numbers from each to provide a route for CVRP. Then we compare the performance of pseudorandom number generators with respect to the total time the random route takes. We also constructed an open-source library github.com/iedmrc/binary-cws-mcs on solving CVRP by M…
The paper presents a two-stage stochastic program to model a routing problem involving an Unmanned Aerial Vehicle (UAV) in the context of patrolling missions. In particular, given a set of targets and a set of supplemental targets corresponding to each target, the first stage decisions involve finding the sequence in which the vehicle has to visit the set of targets. Upon reaching each target, the UAV collects information and if the operator of the UAV deems that the information collected is not of sufficient fidelity, then the UAV has to visit all the supplemental targets corresponding to tha…
The past decade has seen a substantial increase in the use of small unmanned aerial vehicles (UAVs) in both civil and military applications. This article addresses an important aspect of refueling in the context of routing multiple small UAVs to complete a surveillance or data collection mission. Specifically, this article formulates a multiple-UAV routing problem with the refueling constraint of minimizing the overall fuel consumption for all of the vehicles as a two-stage stochastic optimization problem with uncertainty associated with the fuel consumption of each vehicle. The two-stage mode…
We study a routing and appointment scheduling problem with uncertain service and travel times arising from home service practice. Specifically, given a set of customers within a service region that an operator needs to serve, we seek to find the operator's route and time schedule. The quality of routing and scheduling decisions is a function of the total operational cost, consisting of customers' waiting time, and the operator's travel time, idle time, and overtime. We propose and rigorously analyze a stochastic programming model and two distributionally robust optimization (DRO) models to sol…
Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed dynamically with the goal of maximizing the number of served requests. We model the DVRPSR as a multi-stage optimization problem, where the first-stage decision defines route plans for serving scheduled requests. Our main contributions are knapsack-based linear models to approximate accurately the expected reward-to-go, measured as the number of accepted requests, …
This article aims to develop novel path planning algorithms required to deploy multiple unmanned vehicles in Global Positioning System (GPS) denied environments. Unmanned vehicles (ground or aerial) are ideal platforms for executing monitoring and data gathering tasks in civil infrastructure management, agriculture, public safety, law enforcement, disaster relief and transportation. Significant advancement in the area of path planning for unmanned vehicles over the last decade has resulted in a suite of algorithms that can handle heterogeneity, motion and other on-board resource constraints fo…
Rail-guided vehicles (RGVs) are widely employed in automated freight handling system (AFHS) to transport surging air cargo. Energy-efficient routing of such vehicles is of great interest for both financial and environmental sustainability. Given a multi-capacity RGV working on a linear track in AFHS, we consider its optimal routing under two-sided loading/unloading (TSLU) operations, in which energy consumption is minimized under conflict-avoidance and time window constraints. The energy consumption takes account of routing-dependent gross weight and dynamics of the RGV, and the conflict-avoid…
In the Home Service Assignment, Routing, and Appointment scheduling (H-SARA) problem, a set of homogeneous service teams must visit a set of customers. The home service provider needs to decide how many teams to hire (i.e., sizing problem), how to assign service teams to customers (i.e., assignment problem), how to route service teams (i.e., vehicle routing problem),and how to schedule the appointment times for the customers (i.e., appointment scheduling problem) such that the total cost is minimized. To tackle the H-SARA problem, we propose an efficient solution method that comprises two stag…
Huazhong University of Science and Technology（华中科技大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Vehicle routing is a well-known optimization research topic with significant practical importance. Among different approaches to solving vehicle routing, heuristics can produce a satisfactory solution at a reasonable computational cost. Consequently, much effort has been made in the past decades to develop vehicle routing heuristics. In this article, we systematically survey the existing vehicle routing heuristics, particularly on works carried out in recent years. A classification of vehicle routing heuristics is presented, followed by a review of their methodologies, recent developments, and…
Humanitarian logistics service providers have two major responsibilities immediately after a disaster: locating trapped people and routing aid to them. These difficult operations are further hindered by failures in the transportation and telecommunications networks, which are often rendered unusable by the disaster at hand. In this work, we propose a two-echelon vehicle routing framework for performing these operations using aerial uncrewed autonomous vehicles (UAVs or drones) to address the issues associated with these failures. In our proposed framework, we assume that ground vehicles cannot…
Branch-Price-and-Cut Accelerated with a Pricing for Integrality Heuristic for the Electrical Vehicle Routing Problem with Time Windows and Charging Time Slots
The Vehicle Routing Problem with Time-Windows (VRPTW) is an important problem in allocating resources on networks in time and space. We present in this paper a Deterministic Annealing (DA)-based approach to solving the VRPTW with its aspects of routing and scheduling, as well as to model additional constraints of heterogeneous vehicles and shipments. This is the first time, to our knowledge, that a DA approach has been used for problems in the class of the VRPTW. We describe how the DA approach can be adapted to generate an effective heuristic approach to the VRPTW. Our DA approach is also des…
In this research, a new variant of the vehicle routing problem with time windows is addressed. The nodes associated with the customers are related to each other through AND/OR precedence constraints. The objective is minimizing the total traveling and service time. This generalization is necessary for problems where the visiting node sequence is defined according to the AND/OR relations, such as picker routing problems. We propose a Mixed Integer Linear Programming model to solve small-scale instances extended from the well-known Solomon benchmark. A meta-heuristic algorithm based on the hybri…
We consider a cooperative vehicle routing problem for surveillance and reconnaissance missions with communication constraints between the vehicles. We propose a framework which involves a ground vehicle and an aerial vehicle; the vehicles travel cooperatively satisfying the communication limits, and visit a set of targets. We present a mixed integer linear programming (MILP) formulation and develop a branch-and-cut algorithm to solve the path planning problem for the ground and air vehicles. The effectiveness of the proposed approach is corroborated through extensive computational experiments …
We present an analytical upper bound on the number of required vehicles for vehicle routing problems with split deliveries and any number of capacitated depots. We show that a fleet size greater than the proposed bound is not achievable based on a set of common assumptions. This property of the upper bound is proved through a dynamic programming approach. We also discuss the validity of the bound for a wide variety of routing problems with or without split deliveries.
This work proposes a first extensive analysis of the Vehicle Routing Problem with Fractional Objective Function (vrpfof). We investigate how the principal techniques used either in the context of fractional programming or in the context of vehicle routing problems interact. We present new dual and primal bounding procedures which have been incorporated in an exact method. The method proposed allows to extend specific variants of \vrp\ to their counterpart with a fractional objective function. Extensive numerical experiments prove the validity of our approach.
We present a set of new instances of the maximum weight independent set problem. These instances are derived from a real-world vehicle routing problem and are challenging to solve in part because of their large size. We present instances with up to 881 thousand nodes and 383 million edges.
We introduce BROUTE, a benchmark suite for vehicle routing optimization algorithms. We define a selection of algorithms traditionally used in vehicle routing optimization. They capture essential features that are also relevant in optimization algorithms for different application domains, like local search move evaluation, memory allocation, dynamic programming, or insertion and deletion from a list. Each algorithm is deterministic. We implement these benchmark algorithms using a selection of programming languages and different data structures. BROUTE is free, open-source, and can be used to in…
Optimization of on-demand transportation systems and ride-sharing services involves solving a class of complex vehicle routing problems with pickup and delivery with time windows (VRPPDTW). This paper first proposes a new time-discretized multi-commodity network flow model for the VRPPDTW based on the integration of vehicles carrying states within space-time transportation networks, so as to allow a joint optimization of passenger-to-vehicle assignment and turn-by-turn routing in congested transportation networks. Our three-dimensional state-space-time network construct is able to comprehensiv…
We formulate and solve the H-SARA Problem, a Vehicle Routing and Appointment Scheduling Problem motivated by home services management. We assume that travel times, service durations, and customer cancellations are stochastic. We use a two-stage process that first generates teams and routes using a VRP Solver with optional extensions and then uses an MC Scheduler that determines expected arrival times by teams at customers. We further introduce two different models of cancellation and their associated impacts on routing and scheduling. Finally, we introduce the Route Fracture Metaheuristic that…
SNCF, the French public train company, is experimenting to develop new types of transportation services by tackling vehicle routing problems. While many deep learning models have been used to tackle efficiently vehicle routing problems, it is difficult to take into account time related constraints. In this paper, we solve the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and the Capacitated Pickup and Delivery Problem with Time Windows (CPDPTW) with a constructive iterative Deep Learning algorithm. We use an Attention Encoder-Decoder structure and design a novel insertion heur…
We consider a wide family of vehicle routing problem variants with many complex and practical constraints, known as rich vehicle routing problems, which are faced on a daily basis by C.H. Robinson (CHR). Since CHR has many customers, each with distinct requirements, various routing problems with different objectives and constraints should be solved. We propose a set partitioning framework with a number of route generation algorithms, which have shown to be effective in solving a variety of different problems. The proposed algorithms have outperformed the existing technologies at CHR on 10 benc…
We study the strategic decision-making problem of assigning time windows to customers in the context of vehicle routing applications that are affected by operational uncertainty. This problem, known as the Time Window Assignment Vehicle Routing Problem, can be viewed as a two-stage stochastic optimization problem, where time window assignments constitute first-stage decisions, vehicle routes adhering to the assigned time windows constitute second-stage decisions, and the objective is to minimize the expected routing costs. We prove that a sampled deterministic equivalent of this stochastic mod…
The capacitated Vehicle Routing Problem with structured Time Windows (cVRPsTW) is concerned with finding optimal tours for vehicles with given capacity constraints to deliver goods to customers within assigned time windows. In our problem variant these time windows have a special structure, namely they are non-overlapping and each time window holds several customers. This is a reasonable assumption for Attended Home Delivery services. Sweep algorithms are known as simple, yet effective heuristics for the classical capacitated Vehicle Routing Problem. We propose variants of the sweep algorithm …
Different types of formulations are proposed in the literature to model vehicle routing problems. Currently, the most used ones can be fitted into two classes, namely vehicle flow formulations and set partitioning formulations. These types of formulations differ from each other not only due to their variables and constraints but also due to their main features. Vehicle flow formulations have the advantage of being compact models, so general-purpose optimization packages can be used to straightforwardly solve them. However, they typically show weak linear relaxations and have a large number of …
In many applications of vehicle routing, a set of time windows are feasible for each visit, giving rise to the Vehicle Routing Problem with Multiple Time Windows (VRPMTW). We argue that such disjunctions are problematic for many solution methods, and exemplify this using a state of the art Adaptive Large Neighbourhood Search heuristic. VRPMTW comes in two variants depending on whether the time used en route must be minimised. A more compact and corrected mathematical formulation for both variants of the problem is presented, and new best solutions for all but six benchmark instances of VRPMTW …
The electric vehicle routing problem (EVRP) has garnered great interest from researchers and industrialists in an attempt to move from fuel-based vehicles to healthier and more efficient electric vehicles (EVs). While it seems that the EVRP should not be much different from traditional vehicle routing problems (VRPs), challenges like limited cruising time, long charging times, and limited availability of charging facilities for electric vehicles makes all the difference. Previous works target logistics and delivery-related solutions wherein a homogeneous fleet of commercial EVs have to return …
This paper considers an unmanned vehicle-robot pickup and delivery system, in which a self-driving vehicle carrying multiple unmanned robots in the form of the mother ship travels from a depot to a number of stations distributed in a neighborhood to perform multiple pickup and delivery services. First of all, we present it as a Multi-modal Vehicle Routing Problem (MMVRP) with time constraints, which are typical service requirements for grocery and food delivery in practice. We then formulate it as a Mixed Integer Quadratically Con-strained Program (MIQCP) model to determine the optimal integra…
We consider a queue with renewal arrivals and n exponential servers in the Halfin-Whitt heavy traffic regime, where n and the arrival rate increase without bound, so that a critical loading condition holds. Server k serves at rate $μ_k $, and the empirical distribution of the $μ_k $ is assumed to converge weakly. We show that very little information on the service rates is required for a routing mechanism to perform well. More precisely, we construct a routing mechanism that has access to a single sample from the service time distribution of each of $n$ to the power of $1/2 + ε$ randomly selec…
Quantum annealing technologies aim to solve computational optimization and sampling problems. QPU (Quantum Processing Unit) machines such as the D-Wave system use the QUBO (Quadratic Unconstrained Binary Optimization) formula to define model optimization problems for quantum annealing. This machine uses quantum effects to speed up computing time better than classical computers. We propose a vehicle routing problem that can be formulated in the QUBO model as a combinatorial problem, which gives the possible route solutions increases exponentially. The solution aims to optimize the vehicle's jou…
Laboratory of Innovations in Transportation (LiTrans)（交通创新实验室）；Ryerson University（瑞尔森大学）
This study exploits the advancements in information and communication technology (ICT), connected and automated vehicles (CAVs), and sensing, to develop proactive multi-objective eco-routing strategies. For a robust application, several GHG costing approaches are examined. The predictive models for the link level traffic and emission states are developed using long short term memory deep network with exogenous predictors. It is found that proactive routing strategies outperformed the myopic strategies, regardless of the routing objective. Whether myopic or proactive, the multi-objective routin…
Università di Roma La Sapienza（罗马第一大学）；Missouri University of Science and Technology（密苏里科技大学）；University of Klagenfurt（克拉根福大学）；University of Eastern Piedmont（东皮埃蒙特大学）
Unmanned aerial vehicles (UAVs) are aircraft whose flights can be fully autonomous without any provision for human intervention. One of the most useful and promising domains where UAVs can be employed is natural disaster management. In this paper, we focus on an emergency scenario and propose the use of a fleet of UAVs that help rescue teams to individuate people needing help inside an affected area. We model this situation as an original graph theoretical problem called Multi-Depot Multi-Trip Vehicle Routing Problem with Total Completion Times minimization (MDMT-VRP-TCT); we go through some p…
