We study a new variant of the well-studied Vehicle Routing Problem with Time Windows (VRPTW), called the fragility-constrained VRPTW, which assumes that 1) the capacity of a vehicle is organized in multiple identical stacks; 2) all items picked up at a customer are either "fragile" or not; 3) no non-fragile items can be put on top of a fragile item (the fragility constraint) ; and 4) no en-route load rearrangement is possible. We first characterize the feasibility of a route with respect to this fragility constraint. Then, to solve this new problem, we develop an exact branch-price-and-cut (BPC) algorithm that includes a labeling algorithm exploiting this feasibility characterization to efficiently generate feasible routes. This algorithm is benchmarked against another BPC algorithm that deals with the fragility constraint in the column generation master problem through infeasible path cuts. Our computational results show that the former BPC algorithm clearly outperforms the latter in terms of computational time and that the fragility constraint has a greater impact on the optimal solution cost (compared to that of the VRPTW) when vehicle capacity decreases, stack height increases and for a more balance mix of customers with fragile and non-fragile items.
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…
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…
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…
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 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 …
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…
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…
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 Combined Van-and-Mopeds Routing Problem with Time Windows: Formulation, Variants, and Solution Methods
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；INESC-ID Lisboa（里斯本嵌入式与系统创新研究中心）；Dingoo（丁果）；Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa（里斯本理工学院高等工程学院）
In this paper we study a revenue maximization problem for optical routing nodes. We model the routing node as a single server polling model with the aim to assign visit periods (service windows) to the different stations (ports) such that the mean profit per cycle is maximized. Under reasonable assumptions regarding retrial and dropping probabilities of packets the optimization problem becomes a separable concave resource allocation problem, which can be solved using existing algorithms.
The main goal of this paper is to time-effectively route and schedule a fleet of Electric Vehicles (EVs) on a road network in order to serve a set of customers. In particular, we aim to propose an optimized route planning by exploiting the advantages of these vehicles. Nowadays, in fact, electromobility plays a key role for reducing the harmful emissions due, instead, to the use of traditional vehicles. The starting point of this research is represented by the fact that the advanced recent technologies for the EVs allow also partially recharging their batteries. In this work, an Electric Vehic…
Universidad Adolfo Ibáñez（阿道夫·伊瓦涅斯大学）；Universidad Diego Portales（迭戈·波塔莱斯大学）；AGH University of Science and Technology（AGH科技大学）
This study introduces the Territory Design for Dynamic Multi-Period Vehicle Routing Problem with Time Windows (TD-DMPVRPTW), motivated by a real-world application at a food company's distribution center. This problem deals with the design of contiguous and compact territories for delivery of orders from a depot to a set of customers, with time windows, over a multi-period planning horizon. Customers and their demands vary dynamically over time. The problem is modeled as a mixed-integer linear program (MILP) and solved by a proposed heuristic. The heuristic solutions are compared with the propo…
Universidad Adolfo Ibáñez（阿道夫·伊瓦涅斯大学）；Universidad Diego Portales（迭戈·波塔莱斯大学）；AGH University of Science and Technology（AGH科技大学）
We develop a heuristic for the Consistent Vehicle Routing Problem with Time Windows (ConVRPTW), which is motivated by a real-world application at a food company's distribution center. Besides standard VRPTW restrictions, ConVRPTW assigns each customer just one driver to fulfill their orders during the whole multi-period planning horizon. For each driver and period, a route is sought to serve all their customers with positive demand. For each customer, the number of periods between consecutive orders and the ordered quantities are highly irregular. This causes difficulties in the daily routing,…
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…
A Rolling-Space Branch-and-Price Algorithm for the Multi-Compartment Vehicle Routing Problem with Multiple Time Windows
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA（佐治亚理工学院H. Milton Stewart工业与系统工程学院）；Department of Operations and Decision Systems, Université Laval（拉瓦尔大学运营管理与决策系统系）
This study presents a novel approach to the vehicle routing problem by focusing on greenhouse gas emissions and fuel consumption aiming to mitigate adverse environmental effects of transportation. A time-dependent model with time windows is developed to incorporate speed and schedule in transportation. The model considers speed limits for different times of the day in a realistic delivery context. Due to the complexity of solving the model, a simulated annealing algorithm is proposed to find solutions with high quality in a timely manner. Our method can be used in practice to lower fuel consum…
University of Toronto（多伦多大学）；Western University（韦仕敦大学）；University of Waterloo（滑铁卢大学）
The past decade has seen a rapid penetration of electric vehicles (EV) in the market, more and more logistics and transportation companies start to deploy EVs for service provision. In order to model the operations of a commercial EV fleet, we utilize the EV routing problem with time windows (EVRPTW). In this research, we propose an end-to-end deep reinforcement learning framework to solve the EVRPTW. In particular, we develop an attention model incorporating the pointer network and a graph embedding technique to parameterize a stochastic policy for solving the EVRPTW. The model is then traine…
Contextual Stochastic Vehicle Routing with Time Windows
School of Management, Technical University of Munich（慕尼黑工业大学管理学院）；Amazon.com, Inc.（亚马逊公司）；Munich Data Science Institute, Technical University of Munich（慕尼黑工业大学慕尼黑数据科学研究所）；Polytechnique Montréal（蒙特利尔理工学院）
University of Maryland（马里兰大学）；University of Southern California（南加州大学）；Verisk（Verisk公司）；ESG UQAM（魁北克大学蒙特利尔分校 ESG 学院）；GERAD（GERAD研究院）；University of California, Irvine（加州大学欧文分校）；Laminaar（Laminaar公司）
Robots performing tasks in warehouses provide the first example of wide-spread adoption of autonomous vehicles in transportation and logistics. The efficiency of these operations, which can vary widely in practice, are a key factor in the success of supply chains. In this work we consider the problem of coordinating a fleet of robots performing picking operations in a warehouse so as to maximize the net profit achieved within a time period while respecting problem- and robot-specific constraints. We formulate the problem as a weighted set packing problem where the elements in consideration are…
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…
Spatial-temporal-demand clustering for solving large-scale vehicle routing problems with time windows
Logistics and Supply Chain Management, School of Management, Technical University of Munich（物流与供应链管理系，管理学院，慕尼黑技术大学）；Munich Data Science Institute (MDSI), Technical University of Munich（慕尼黑数据科学研究所（MDSI），慕尼黑技术大学）
Grocery home delivery services require customers to be present when their deliveries arrive. Hence, the grocery retailer and the customer must mutually agree on a time window during which the delivery can be guaranteed. This concept is referred to as the Attended Home Delivery (AHD) problem. The phase during which customers place orders, usually through a web service, constitutes the computationally most challenging part of the logistical processes behind such services. The system must determine potential delivery time windows that can be offered to incoming customers and incrementally build t…
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…
The resource recharging station location routing problem is a generalization of the location routing problem with sophisticated and critical resource consumption and recharging constraints. Based on a representation of discretized acyclic resource-space-time networks, we propose a generic formulation to optimize dynamic infrastructure location and routes decisions. The proposed integer linear programming formulation could greatly simplify the modeling representation of time window, resource change, and sub-tour constraints through a well-structured multi-dimensional network. An approximation s…
Electric vehicles (EVs) have been highly favoured as a future transportation mode in the transportation section in recent years. EVs have many advantages compared to traditional transportation, especially the environmental aspect. However, despite many EVs' benefits, operating EVs has limitations in their usage. One of the significant issues is the uncertainty in their driving range. The driving range of EVs is closely related to their energy consumption, which is highly affected by exogenous and endogenous factors. Since those factors are unpredictable, uncertainty in EVs' energy consumption …
We consider a family of Rich Vehicle Routing Problems (RVRP) which have the particularity to combine a heterogeneous fleet with other attributes, such as backhauls, multiple depots, split deliveries, site dependency, open routes, duration limits, and time windows. To efficiently solve these problems, we propose a hybrid metaheuristic which combines an iterated local search with variable neighborhood descent, for solution improvement, and a set partitioning formulation, to exploit the memory of the past search. Moreover, we investigate a class of combined neighborhoods which jointly modify the …
During natural or anthropogenic disasters, humanitarian organizations face a series of time-sensitive tasks. One of the tasks involves picking up critical resources (e.g., first aid kits, blankets, water) from warehouses and delivering them to the affected people. To successfully deliver these items to the people in need, the organization needs to make decisions that range from the quick acquisition of vehicles from the local market, to the preparation of pickup and delivery schedules and vehicle routes. During crises, the supply of vehicles is often limited, their acquisition cost is steep, a…
We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its fleet of cars as a feeder to connect passengers to its high-capacity fleet, which operates on fixed routes. Our goal is to find the optimal set of (bus) routes and corresponding frequencies to maximize the social welfare of the system in a given time window. This generalizes the Line Planning Problem, a widely studied topic in the transportation literature, for…
LMask: Learn to Solve Constrained Routing Problems with Lazy Masking
Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；Department of Statistics and Data Science, University of Pennsylvania（宾夕法尼亚大学统计与数据科学系）
