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 decomposition-based iterative optimization algorithm for traveling salesman problem with drone

This study investigates a new delivery problem that has emerged after the attempts of several e-commerce and logistics firms to deploy drones in their operations to increase efficiency and reduce delivery times. In this problem, a delivery truck that carries a drone on its roof serves customers in coordination with a drone. The drone is considered to complement the truck due to its cost-efficiency and ability to access difficult terrains and to travel without exposure to congestion. This study presents an iterative algorithm that is based on a decomposition approach to minimize delivery completion time. In the first stage of the proposed methodology, the truck route and the customers assigned to the drone are determined. In the second stage, a mixed-integer linear programming model is solved to optimize the drone route by fixing the routing and the assignment decisions that are made in the first stage. Beginning with the shortest truck route, the assignment and the routing decisions are iteratively improved. The solution times of our algorithm are compared with the solution times of the state-of-the-art formulations that are solved by CPLEX. The results demonstrate that our algorithm yields shorter solution times for the instances that we generated with the specified parameters. An optimization-based heuristic algorithm, which obtains solutions for medium-sized instances, is developed by reducing the feasible search area.     

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.     

A decision support system for integrated hazardous materials routing and emergency response decisions

Hazardous materials routing constitutes a critical decision in mitigating the associated transportation risk. This paper presents a decision support system for assessing alternative distribution routes in terms of travel time, risk and evacuation implications while coordinating the emergency response deployment decisions with the hazardous materials routes. The proposed system provides the following functionalities: (i) determination of alternative non-dominated hazardous materials distribution routes in terms of cost and risk minimization, (ii) specification of the hazardous materials first-response emergency service units locations in order to achieve timely response to an accident, and (iii) determination of evacuation paths from the impacted area to designated shelters and estimation of the associated evacuation time. The proposed system has been implemented, used and evaluated for assessing alternative hazardous materials routing decisions within the heavily industrialized area of Thriasion Pedion of Attica, Greece. The implementation of the aforementioned functionalities is based on two new integer programming models for the hazardous materials routing and the emergency response units location problems, respectively. A simplified version of the routing model is solved by an existing heuristic algorithm developed by the authors. A new Lagrangean relaxation heuristic algorithm has been developed for solving the emergency response units location problem. The focus of this paper is on the exposition of the proposed decision support system components and functionalities. Special emphasis is placed on the presentation of the two new mathematical models and the new solution method for the location model.     

A warehouse location-routing problem

The interdependence between distribution center location and vehicle routing has been recognized by both academics and practitioners. However, only few attempts have been made to incorporate routing in location analysis. This paper defines the Warehouse Location-Routing Problem (WLRP) as one of simultaneously solving the DC location and vehicle routing problems. We present a mixed integer programming formulation of the WLRP. Based on this formulation, it can be seen that the WLRP is a generalization of well-known and difficult location and routing problems, such as the Location-Allocation Problem and the Multi-depot Vehicle Dispatch Problem. It is therefore a large and complex problem which cannot be solved using existing mixed-integer programming techniques. We present a heuristic solution method for the WLRP, based on decomposing the problem into three subproblems. The proposed method solves the subproblems in a sequential manner while accounting for the dependence between them. We discuss a large-scale application of the proposed method to a national distribution company at a regional level.     

Multi-fleet ferry service network design with passenger preferences for differential services

This paper investigates a multi-fleet ferry routing and scheduling problem that takes into account ferry services with different operation characteristics and passengers with different preferred arrival time windows. The logit model is used to represent passengers’ service choices. The full problem is formulated as a mixed integer nonlinear programming problem and solved with a heuristic procedure that first fixes the demand and then decomposes the resultant model by ferry services. At each iteration of the algorithm, the demand is updated and the relaxed problem is re-solved. Numerical results for the case of ferry service network design in Hong Kong are provided to illustrate the properties of the model and the performance of the heuristic.     

Liner shipping network design with emission control areas: A genetic algorithm-based approach

To curb emissions, containerized shipping lines face the traditional trade-off between cost and emissions (CO₂ and SO_x) reduction. This paper considers this element in the context of liner service design and proposes a mixed integer linear programming (MILP) model based on a multi-commodity pickup and delivery arc-flow formulation. The objective is to maximize the profit by selecting the ports to be visited, the sequence of port visit, the cargo flows between ports, as well as the number/operating speeds of vessels on each arc of the selected route. The problem also considers that Emission Control Areas (ECAs) exist in the liner network and accounts for the vessel carrying capacity. In addition to using the MILP solver of CPLEX, we develop in the paper a specific genetic algorithm (GA) based heuristic and show that it gives the possibility to reach an optimal solution when solving large size instances.     

A range-restricted recharging station coverage model for drone delivery service planning

Unmanned Aerial Vehicles (UAVs) are attracting significant interest for delivery service of small packages in urban areas. The limited flight range of electric drones powered by batteries or fuel cells requires refueling or recharging stations for extending coverage to a wider area. To develop such service, optimization methods are needed for designing a network of station locations and delivery routes. Unlike ground-transportation modes, however, UAVs do not follow a fixed network but rather can fly directly through continuous space. But, paths must avoid barriers and other obstacles. In this paper, we propose a new location model to support spatially configuring a system of recharging stations for commercial drone delivery service, drawing on literature from planar-space routing, range-restricted flow-refueling location, and maximal coverage location. We present a mixed-integer programming formulation and an efficient heuristic algorithm, along with results for a large case study of Phoenix, AZ to demonstrate the effectiveness and efficiency of the model.     

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.     

Designing an integrated distribution system for catering services for high-speed railways: A three-echelon location routing model with tight time windows and time deadlines

An emerging task in catering services for high-speed railways (CSHR) is to design a distribution system for the delivery of high-quality perishable food products to trains in need. This paper proposes a novel model for integrating location decision making with daily rail catering operations, which are affected by various aspects of rail planning, to meet time-sensitive passenger demands. A three-echelon location routing problem with time windows and time budget constraints (3E-LRPTWTBC) is thus proposed toward formulating this integrated distribution system design problem. This model attempts to determine the capacities/locations of distribution centers and to optimize the number of meals delivered to stations. The model also attempts to generate a schedule for refrigerated cars traveling from distribution centers to rail stations for train loading whereby meals can be catered to trains within tight time windows and sold before a specified time deadline. By relaxing the time-window constraints, a relaxation model that can be solved using an off-the-shelf mixed integer programming (MIP) solver is obtained to provide a lower bound on the 3E-LRPTWTBC. A hybrid cross entropy algorithm (HCEA) is proposed to solve the 3E-LRPTWTBC. A small-scale case study is implemented, which reveals a 9.3% gap between the solution obtained using the HCEA and that obtained using the relaxation model (RM). A comparative analysis of the HCEA and an exhaustive enumeration algorithm indicates that the HCEA shows good performance in terms of computation time. Finally, a case study considering 156 trains on the Beijing-Shanghai high-speed corridor and a large-scale case study considering 1130 trains on the Chinese railway network are addressed in a comprehensive study to demonstrate the applicability of the proposed models and algorithm.     

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.     

Biofuel refinery location and supply chain planning under traffic congestion

This research focuses on planning biofuel refinery locations where the total system cost for refinery investment, feedstock and product transportation and public travel is minimized. Shipment routing of both feedstock and product in the biofuel supply chain and the resulting traffic congestion impact are incorporated into the model to decide optimal locations of biofuel refineries. A Lagrangian relaxation based heuristic algorithm is introduced to obtain near-optimum feasible solutions efficiently. To further improve optimality, a branch-and-bound framework (with linear programming relaxation and Lagrangian relaxation bounding procedures) is developed. Numerical experiments with several testing examples demonstrate that the proposed algorithms solve the problem effectively. An empirical Illinois case study and a series of sensitivity analyses are conducted to show the effects of highway congestion on refinery location design and total system costs.     

On activity-based network design problems

This paper examines network design where OD demand is not known a priori, but is the subject of responses in household or user itinerary choices to infrastructure improvements. Using simple examples, we show that falsely assuming that household itineraries are not elastic can result in a lack in understanding of certain phenomena; e.g., increasing traffic even without increasing economic activity due to relaxing of space–time prism constraints, or worsening of utility despite infrastructure investments in cases where household objectives may conflict. An activity-based network design problem is proposed using the location routing problem (LRP) as inspiration. The bilevel formulation includes an upper level network design and shortest path problem while the lower level includes a set of disaggregate household itinerary optimization problems, posed as household activity pattern problem (HAPP) (or in the case with location choice, as generalized HAPP) models. As a bilevel problem with an NP-hard lower level problem, there is no algorithm for solving the model exactly. Simple numerical examples show optimality gaps of as much as 5% for a decomposition heuristic algorithm derived from the LRP. A large numerical case study based on Southern California data and setting suggest that even if infrastructure investments do not result in major changes in link investment decisions compared to a conventional model, the results provide much higher resolution temporal OD information to a decision maker. Whereas a conventional model would output the best set of links to invest given an assumed OD matrix, the proposed model can output the same best set of links, the same daily OD matrix, and a detailed temporal distribution of activity participation and travel from which changes in peak period OD patterns can be observed.     

Joint optimization of freight facility location and pavement infrastructure rehabilitation under network traffic equilibrium

Establishment of industry facilities often induces heavy vehicle traffic that exacerbates congestion and pavement deterioration in the neighboring highway network. While planning facility locations and land use developments, it is important to take into account the routing of freight vehicles, the impact on public traffic, as well as the planning of pavement rehabilitation. This paper presents an integrated facility location model that simultaneously considers traffic routing under congestion and pavement rehabilitation under deterioration. The objective is to minimize the total cost due to facility investment, transportation cost including traffic delay, and pavement life-cycle costs. Building upon analytical results on optimal pavement rehabilitation, the problem is formulated into a bi-level mixed-integer non-linear program (MINLP), with facility location, freight shipment routing and pavement rehabilitation decisions in the upper level and traffic equilibrium in the lower level. This problem is then reformulated into an equivalent single-level MINLP based on Karush–Kuhn–Tucker (KKT) conditions and approximation by piece-wise linear functions. Numerical experiments on hypothetical and empirical network examples are conducted to show performance of the proposed algorithm and to draw managerial insights.     

Ferry service network design: optimal fleet size,routing, and scheduling

The study formulated a ferry network design problem by considering the optimal fleet size, routing, and scheduling for both direct and multi-stop services. The objective function combines both the operator and passengers’ performance measures. Mathematically, the model is formulated as a mixed integer multiple origin–destination network flow problem with ferry capacity constraints. To solve this problem of practical size, this study developed a heuristic algorithm that exploits the polynomial-time performance of shortest path algorithms. Two scenarios of ferry services in Hong Kong were solved to demonstrate the performance of the heuristic algorithm. The results showed that the heuristic produced solutions that were within 1.3% from the CPLEX optimal solutions. The computational time is within tens of seconds even for problem size that is beyond the capability of CPLEX.     

Solution methods for the taxi pooling problem

In Taiwan, taxi pooling is currently performed by some taxi companies using a trial-and-error experience-based method, which is neither effective nor efficient. There is, however, little in the literature on effective models and solution methods for solving the taxi pooling problem. Thus, in this study we employ network flow techniques and a mathematical programming method to develop a taxi pooling solution method. This method is composed of three models. First, a fleet routing/scheduling model is constructed to produce fleet/passenger routes and schedules. A solution algorithm, based on Lagrangian relaxation, a sub-gradient method and a heuristic to find the upper bound of the solution, is proposed to solve the fleet routing/scheduling model. Then, two single taxi-passenger matching models are constructed with the goals of decreasing number of passenger transfers and matching all passengers and taxis. These two taxi-passenger matching models are directly solved using a mathematical programming solver. For comparison with the solution method, we also develop another heuristic by modifying a heuristic recently proposed for solving a one-to-many taxi pooling problem. The performance of the solution method and the additional heuristic are evaluated by carrying out a case study using real data and suitable assumptions. The test results show that these two solution methods could be useful in practice.     

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 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.     

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.