The two-echelon time-constrained vehicle routing problem in linehaul-delivery systems

Most of the studies address issues relating to the delivery from satellites to customers, which is throughout the end part of the linehaul-delivery system. Differing from the long-term strategic problems including the two-echelon vehicle routing problem (2E-VRP), the two-echelon location routing problem (2E-LRP) and the truck and trailer routing problem (TTRP) which make location decisions in depots or satellites, the paper introduces a short-term tactical problem named the two-echelon time-constrained vehicle routing problem in linehaul-delivery systems (2E-TVRP) that does not involve location decisions. The linehaul level and the delivery level are linked through city distribution centers (CDCs) located on the outskirts of cities. The 2E-TVRP has inter-CDC linehaul on the first level and urban delivery from CDCs to satellites on the second level. Vehicle routes on different levels are interacted by time constraints. A mixed integer nonlinear programming model for the 2E-TVRP is put forward, and a mixed integer linear programming model is used as the benchmark model. The Clarke and Wright savings heuristic algorithm (CW) improved by a local search phase is adopted. The 2E-TVRP formulations and the heuristic algorithm are tested by using 140 randomly-generated instances with up to 10 CDCs and 500 satellites. The computational results indicate that the heuristic can effectively solve various instances of the 2E-TVRP.     

Scheduling railway freight delivery appointments using a bid price approach

This paper proposes a method for establishing aggressive but achievable delivery appointment times for railroad shipments, taking into account individual customer needs and forecasted available train capacity. The concept of scheduling appointment times is directly patterned after current motor carrier industry practice, so that customers can plan for rail or truck deliveries in the same way.A shipment routing problem is decomposed into a deterministic “dynamic car scheduling” (DCS) process for shipments already accepted and a stochastic “train segment pricing” (TSP) process for forecasting future demands which have not yet called in and for which delivery appointments have yet to be scheduled. Both are formulated as multi-commodity network flow (MCNF) problems, where each shipment is treated as a separate commodity. Gain coefficients represent recapture probabilities that a specific customer will accept a carrier’s service offer.A comparison with a widely used revenue management formulation is given. A Lagrangian heuristic for obtaining a primal solution is also described. The problem is solved within a 1% gap using the subgradient algorithm.     

Integrated scheduling of m-truck,m-drone,and m-depot constrained by time-window,drop-pickup,and m-visit using constraint programming

The idea of deploying unmanned aerial vehicles, also known as drones, for final-mile delivery in logistics operations has vitalized this new research stream. One conceivable scenario of using a drone in conjunction with a traditional delivery truck to distribute parcels is discussed in earlier literature and termed the parallel drone scheduling traveling salesman problem (PDSTSP). This study extends the problem by considering two different types of drone tasks: drop and pickup. After a drone completes a drop, the drone can either fly back to depot to deliver the next parcels or fly directly to another customer for pickup. Integrated scheduling of multiple depots hosting a fleet of trucks and a fleet of drones is further studied to achieve an operational excellence. A vehicle that travels near the boundary of the coverage area might be more effective to serve customers that belong to the neighboring depot. This problem is uniquely modeled as an unrelated parallel machine scheduling with sequence dependent setup, precedence-relationship, and reentrant, which gives us a framework to effectively consider those operational challenges. A constraint programming approach is proposed and tested with problem instances of m-truck, m-drone, m-depot, and hundred-customer distributed across an 8-mile square region.     

The Time Dependent Traveling Salesman Planning Problem in Controlled Airspace

The integration of drones into civil airspace is one of the most challenging problems for the automation of the controlled airspace, and the optimization of the drone route is a key step for this process. In this paper, we optimize the route planning of a drone mission that consists of departing from an airport, flying over a set of mission way points and coming back to the initial airport. We assume that during the mission a set of piloted aircraft flies in the same airspace and thus the cost of the drone route depends on the air traffic and on the avoidance maneuvers used to prevent possible conflicts. Two air traffic management techniques, i.e., routing and holding, are modeled in order to maintain a minimum separation between the drone and the piloted aircraft. The considered problem, called the Time Dependent Traveling Salesman Planning Problem in Controlled Airspace (TDTSPPCA), relates to the drone route planning phase and aims to minimize the total operational cost. Two heuristic algorithms are proposed for the solution of the problem. A mathematical formulation based on a particular version of the Time Dependent Traveling Salesman Problem, which allows holdings at mission way points, and a Branch and Cut algorithm are proposed for solving the TDTSPPCA to optimality. An additional formulation, based on a Travelling Salesman Problem variant that uses specific penalties to model the holding times, is proposed and a Cutting Plane algorithm is designed. Finally, computational experiments on real-world air traffic data from Milano Linate Terminal Maneuvering Area are reported to evaluate the performance of the proposed formulations and of the heuristic algorithms.     

A tailored branch-and-price approach for a joint tramp ship routing and bunkering problem

This paper deals with a practical tramp ship routing problem while taking into account different bunker prices at different ports, which is called the joint tramp ship routing and bunkering (JSRB) problem. Given a set of cargoes to be transported and a set of ports with different bunker prices, the proposed problem determines how to route ships to carry the cargoes and the amount of bunker to purchase at each port, in order to maximize the total profit. After building an integer linear programming model for the JSRB problem, we propose a tailored branch-and-price (B&P) solution approach. The B&P approach incorporates an efficient method for obtaining the optimal bunkering policy and a novel dominance rule for detecting inefficient routing options. The B&P approach is tested with randomly generated large-scale instances derived from real-world planning problems. All of the instances can be solved efficiently. Moreover, the proposed approach for the JSRB problem outperforms the conventional sequential planning approach and can incorporate the prediction of future cargo demand to avoid making myopic decisions.     

Ant colony optimization for the real-time train routing selection problem

This paper deals with the real-time problem of scheduling and routing trains in a railway network. In the related literature, this problem is usually solved starting from a subset of routing alternatives and computing the near-optimal solution of the simplified routing problem. We study how to select the best subset of routing alternatives for each train among all possible alternatives. The real-time train routing selection problem is formulated as an integer linear programming formulation and solved via an algorithm inspired by the ant colonies’ behavior. The real-time railway traffic management problem takes as input the best subset of routing alternatives and is solved as a mixed-integer linear program. The proposed methodology is tested on two practical case studies of the French railway infrastructure: the Lille terminal station area and the Rouen line. The computational experiments are based on several practical disturbed scenarios. Our methodology allows the improvement of the state of the art in terms of the minimization of train consecutive delays. The improvement is around 22% for the Rouen instances and around 56% for the Lille instances.     

The time-dependent vehicle routing problem with soft time windows and stochastic travel times

This paper studies a vehicle routing problem with time-dependent and stochastic travel times. In our problem setting, customers have soft time windows. A mathematical model is used in which both efficiency for service as well as reliability for customers are taken into account. Depending on whether service times are included or not, we consider two versions of this problem. Two metaheuristics are built: a Tabu Search and an Adaptive Large Neighborhood Search. We carry out our experiments for well-known problem instances and perform comprehensive analyses on the numerical results in terms of the computational time and the solution quality. Experiments confirm that the proposed procedure is effective to obtain very good solutions to be performed in real-life environment.     

An iterative route construction and improvement algorithm for the vehicle routing problem with soft time windows

The solution of routing problems with soft time windows has valuable practical applications. Soft time window solutions are needed when: (a) the number of routes needed for hard time windows exceeds the number of available vehicles, (b) a study of cost-service tradeoffs is required, or (c) the dispatcher has qualitative information regarding the relative importance of hard time-window constraints across customers. This paper proposes a new iterative route construction and improvement algorithm to solve vehicle routing problems with soft time windows. Due to its modular and hierarchical design, the solution algorithm is intuitive and able to accommodate general cost and penalty functions. Experimental results indicate that the average run time performance is of order O(n²). The solution quality and computational time of the new algorithm has been compared against existing results on benchmark problems. The presented algorithm has improved thirty benchmark problem solutions for the vehicle routing problems with soft time windows.     

A differential evolution approach for the vehicle routing problem with backhauls and time windows

This paper presents a differential evolution algorithm (DEA) to solve a vehicle routing problem with backhauls and time windows (VRPBTW) and applied for a catering firm. VRPBTW is an extension of the vehicle routing problem, which includes capacity and time window constraints. In this problem, customers are divided into two subsets: linehaul and backhaul. Each vehicle starts from a depot and goods are delivered from the depot to the linehaul customers. Goods are subsequently brought back to the depot from the backhaul customers. The objective is to minimize the total distance that satisfies all of the constraints. The problem is formulated using mixed integer programming and solved using DEA. Proposed algorithm is tested with several benchmark problems to demonstrate effectiveness and efficiency of the algorithm and results show that our proposed algorithm can find superior solutions for most of the problems in comparison with the best known solutions. Hence, DEA was carried out for catering firm to minimize total transportation costs. Copyright © 2013 John Wiley & Sons, Ltd.     

Dynamic green bike repositioning problem – A hybrid rolling horizon artificial bee colony algorithm approach

This paper introduces a new dynamic green bike repositioning problem (DGBRP) that simultaneously minimizes the total unmet demand of the bike-sharing system and the fuel and CO₂ emission cost of the repositioning vehicle over an operational period. The problem determines the route and the number of bikes loaded and unloaded at each visited node over a multi-period operational horizon during which the cycling demand at each node varies from time to time. To handle the dynamic nature of the problem, this study adopts a rolling horizon approach to break down the proposed problem into a set of stages, in which a static bike repositioning sub-problem is solved in each stage. An enhanced artificial bee colony (EABC) algorithm and a route truncation heuristic are jointly used to optimize the route design in each stage, and the loading and unloading heuristic is used to tackle the loading and unloading sub-problem along the route in a given stage. Numerical results show that the EABC algorithm outperforms Genetic Algorithm in solving the routing sub-problem. Computation experiments are performed to illustrate the effect of the stage duration on the two objective values, and the results show that longer stage duration leads to higher total unmet demand and total fuel and CO₂ emission cost. Numerical studies are also performed to illustrate the effects of the weight and the loading and unloading times on the two objective values and the tradeoff between the two objectives.     

Partial recharge strategies for the electric vehicle routing problem with time windows

The Electric Vehicle Routing Problem with Time Windows (EVRPTW) is an extension to the well-known Vehicle Routing Problem with Time Windows (VRPTW) where the fleet consists of electric vehicles (EVs). Since EVs have limited driving range due to their battery capacities they may need to visit recharging stations while servicing the customers along their route. The recharging may take place at any battery level and after the recharging the battery is assumed to be full. In this paper, we relax the full recharge restriction and allow partial recharging (EVRPTW-PR), which is more practical in the real world due to shorter recharging duration. We formulate this problem as a 0–1 mixed integer linear program and develop an Adaptive Large Neighborhood Search (ALNS) algorithm to solve it efficiently. We apply several removal and insertion mechanisms by selecting them dynamically and adaptively based on their past performances, including new mechanisms specifically designed for EVRPTW and EVRPTW-PR. These new mechanisms include the removal of the stations independently or along with the preceding or succeeding customers and the insertion of the stations with determining the charge amount based on the recharging decisions. We test the performance of ALNS by using benchmark instances from the recent literature. The computational results show that the proposed method is effective in finding high quality solutions and the partial recharging option may significantly improve the routing decisions.     

Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Hazardous materials routing and scheduling decisions involve the determination of the minimum cost and/or risk routes for servicing the demand of a given set of customers. This paper addresses the bicriterion routing and scheduling problem arising in hazardous materials distribution planning. Under the assumption that the cost and risk attributes of each arc of the underlying transportation network are time-dependent, the proposed routing and scheduling problem pertains to the determination of the non-dominated time-dependent paths for servicing a given and fixed sequence of customers (intermediate stops) within specified time windows. Due to the heavy computational burden for solving this bicriterion problem, an alternative algorithm is proposed that determines the k-shortest time-dependent paths. Moreover an algorithm is provided for solving the bicriterion problem. The proximity of the solutions of the k-shortest time-dependent path problem with the non-dominated solutions is assessed on a set of problems developed by the authors.     

The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery

Once limited to the military domain, unmanned aerial vehicles are now poised to gain widespread adoption in the commercial sector. One such application is to deploy these aircraft, also known as drones, for last-mile delivery in logistics operations. While significant research efforts are underway to improve the technology required to enable delivery by drone, less attention has been focused on the operational challenges associated with leveraging this technology. This paper provides two mathematical programming models aimed at optimal routing and scheduling of unmanned aircraft, and delivery trucks, in this new paradigm of parcel delivery. In particular, a unique variant of the classical vehicle routing problem is introduced, motivated by a scenario in which an unmanned aerial vehicle works in collaboration with a traditional delivery truck to distribute parcels. We present mixed integer linear programming formulations for two delivery-by-drone problems, along with two simple, yet effective, heuristic solution approaches to solve problems of practical size. Solutions to these problems will facilitate the adoption of unmanned aircraft for last-mile delivery. Such a delivery system is expected to provide faster receipt of customer orders at less cost to the distributor and with reduced environmental impacts. A numerical analysis demonstrates the effectiveness of the heuristics and investigates the tradeoffs between using drones with faster flight speeds versus longer endurance.     

The two-echelon time-constrained vehicle routing problem in linehaul-delivery systems considering carbon dioxide emissions

Multi-echelon distribution strategy is primarily to alleviate the environmental (e.g., energy consumption and emissions) consequence of logistics operations. Differing from the long-term strategic problems (e.g., the two-echelon vehicle routing problem (2E-VRP), the two-echelon location routing problem (2E-LRP) and the truck and trailer routing problem (TTRP)) that make location decisions in depots or satellites, the paper introduces a short-term tactical problem named the two-echelon time-constrained vehicle routing problem in linehaul-delivery systems (2E-TVRP) considering carbon dioxide (CO₂) emissions. The linehaul level and the delivery level are linked through city distribution centers (CDCs). The 2E-TVRP, which takes CO₂ emissions per ton-kilometer as the objective, has inter-CDC linehaul on the 1st level and delivery from CDCs to satellites on the 2nd level. The Clarke and Wright savings heuristic algorithm (CW) improved by a local search phase is put forward. The case study shows the applicability of the model to real-life problems. The results suggest that the vehicle scheduling provided by the 2E-TVRP is promising to reduce the CO₂ emissions per ton-kilometer of the linehaul-delivery system. Adjusting the central depot location or developing the loaded-semitrailer demand among O-D pairs to eliminate empty-running of tractors will contribute to reduce the CO₂ emission factor.     

A set-covering model for a bidirectional multi-shift full truckload vehicle routing problem

This paper introduces a bidirectional multi-shift full truckload transportation problem with operation dependent service times. The problem is different from the previous container transport problems and the existing approaches for container transport problems and vehicle routing pickup and delivery are either not suitable or inefficient. In this paper, a set covering model is developed for the problem based on a novel route representation and a container-flow mapping. It was demonstrated that the model can be applied to solve real-life, medium sized instances of the container transport problem at a large international port. A lower bound of the problem is also obtained by relaxing the time window constraints to the nearest shifts and transforming the problem into a service network design problem. Implications and managerial insights of the results by the lower bound results are also provided.     

Design and development of a hybrid ant colony-variable neighbourhood search algorithm for a multi-depot green vehicle routing problem

The traditional distribution planning problem in a supply chain has often been studied mainly with a focus on economic benefits. The growing concern about the effects of anthropogenic pollutions has forced researchers and supply chain practitioners to address the socio-environmental concerns. This research study focuses on incorporating the environmental impact on route design problem. In this work, the aim is to integrate both the objectives, namely economic cost and emission cost reduction for a capacitated multi-depot green vehicle routing problem. The proposed models are a significant contribution to the field of research in green vehicle routing problem at the operational level. The formulated integer linear programming model is solved for a set of small scale instances using LINGO solver. A computationally efficient Ant Colony Optimization (ACO) based meta-heuristic is developed for solving both small scale and large scale problem instances in reasonable amount of time. For solving large scale instances, the performance of the proposed ACO based meta-heuristic is improved by integrating it with a variable neighbourhood search.     

A multiple type bike repositioning problem

This paper investigates a new static bicycle repositioning problem in which multiple types of bikes are considered. Some types of bikes that are in short supply at a station can be substituted by other types, whereas some types of bikes can occupy the spaces of other types in the vehicle during repositioning. These activities provide two new strategies, substitution and occupancy, which are examined in this paper. The problem is formulated as a mixed-integer linear programming problem to minimize the total cost, which consists of the route travel cost, penalties due to unmet demand, and penalties associated with the substitution and occupancy strategies. A combined hybrid genetic algorithm is proposed to solve this problem. This solution algorithm consists of (i) a modified version of a hybrid genetic search with adaptive diversity control to determine routing decisions and (ii) a proposed greedy heuristic to determine the loading and unloading instructions at each visited station and the substitution and occupancy strategies. The results show that the proposed method can provide high-quality solutions with short computing times. Using small examples, this paper also reveals problem properties and repositioning strategies in bike sharing systems with multiple types of bikes.     

An evolutionary local search for the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints

This study introduces a new practical variant of the combined routing and loading problem called the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints (3L-FCVRP). It presents a meta-heuristic algorithm for solving the problem. The aim is to design routes for a fleet of homogeneous vehicles that will serve all customers, whose demands are formed by a set of three-dimensional, rectangular, weighted items. Unlike the well-studied capacitated vehicle routing problem with 3D loading constraints (3L-CVRP), the objective of the 3L-FCVRP is to minimize total fuel consumption rather than travel distance. The fuel consumption rate is assumed to be proportionate to the total weight of the vehicle. A route is feasible only if a feasible loading plan to load the demanded items into the vehicle exists and the loading plan must satisfy a set of practical constraints.To solve this problem, the evolutionary local search (ELS) framework incorporating the recombination method is used to explore the solution space, and a new heuristic based on open space is used to examine the feasibility of the solutions. In addition, two special data structures, Trie and Fibonacci heap, are adopted to speed up the procedure. To verify the effectiveness of our approach, we first test the ELS on the 3L-CVRP, which can be seen as a special case of the 3L-FCVRP. The results demonstrate that on average ELS outperforms all of the existing approaches and improves the best-known solutions for most instances. Then, we generate data for 3L-FCVRP and report the detailed results of the ELS for future comparisons.     

Comparison of energy demands of drone-based and ground-based parcel delivery services

Drones are one of the most intensively studied technologies in logistics in recent years. They combine technological features matching current trends in transport industry and society like autonomy, flexibility, and agility. Among the various concepts for using drones in logistics, parcel delivery is one of the most popular application scenarios. Companies like Amazon test drones particularly for last-mile delivery intending to achieve both reducing total cost and increasing customer satisfaction by fast deliveries. As drones are electric vehicles, they are also often claimed to be an eco-friendly mean of transportation.In this paper an energy consumption model for drones is proposed to describe the energy demand for drone deliveries depending on environmental conditions and the flight pattern. The model is used to simulate the energy demand of a stationary parcel delivery system which serves a set customers from a depot. The energy consumed by drones is compared to the energy demand of Diesel trucks and electric trucks serving the same customers from the same depot.The results indicate that switching to a solely drone-based parcel delivery system is not worthwhile from an energetic perspective in most scenarios. A stationary drone-based parcel delivery system requires more energy than a truck-based parcel delivery system particularly in urban areas where customer density is high and truck tours are comparatively short. In rather rural settings with long distances between customers, a drone-based parcel delivery system creates an energy demand comparable to a parcel delivery system with electric trucks provided environmental conditions are moderate.     

Congestion-aware system optimal route choice for shared autonomous vehicles

We study the shared autonomous vehicle (SAV) routing problem while considering congestion. SAVs essentially provide a dial-a-ride service to travelers, but the large number of vehicles involved (tens of thousands of SAVs to replace personal vehicles) results in SAV routing causing significant congestion. We combine the dial-a-ride service constraints with the linear program for system optimal dynamic traffic assignment, resulting in a congestion-aware formulation of the SAV routing problem. Traffic flow is modeled through the link transmission model, an approximate solution to the kinematic wave theory of traffic flow. SAVs interact with travelers at origins and destinations. Due to the large number of vehicles involved, we use a continuous approximation of flow to formulate a linear program. Optimal solutions demonstrate that peak hour demand is likely to have greater waiting and in-vehicle travel times than off-peak demand due to congestion. SAV travel times were only slightly greater than system optimal personal vehicle route choice. In addition, solutions can determine the optimal fleet size to minimize congestion or maximize service.