An integrated modelling approach for the bicriterion vehicle routing and scheduling problem with environmental considerations

The consideration of pollution in routing decisions gives rise to a new routing framework where measures of the environmental implications are traded off with business performance measures. To address this type of routing decisions, we formulate and solve a bi-objective time, load and path-dependent vehicle routing problem with time windows (BTL-VRPTW). The proposed formulation incorporates a travel time model representing realistically time varying traffic conditions. A key feature of the problem under consideration is the need to address simultaneously routing and path finding decisions. To cope with the computational burden arising from this property of the problem we propose a network reduction approach. Computational tests on the effect of the network reduction approach on determining non-dominated solutions are reported. A generic solution framework is proposed to address the BTL-VRPTW. The proposed framework combines any technique that creates capacity-feasible routes with a routing and scheduling method that aims to convert the identified routes to problem solutions. We show that transforming a set of routes to BTL-VRPTW solutions is equivalent to solving a bi-objective time dependent shortest path problem on a specially structured graph. We propose a backward label setting technique to solve the emerging problem that takes advantage of the special structure of the graph. The proposed generic solution framework is implemented by integrating the routing and scheduling method into an Ant Colony System algorithm. The accuracy of the proposed algorithm was assessed on the basis of its capability to determine minimum travel time and fuel consumption solutions. Although the computational results are encouraging, there is ample room for future research in algorithmic advances on addressing the proposed problem.     

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.     

Train routing and timetabling problem for heterogeneous train traffic with switchable scheduling rules

This paper proposes a mathematical model for the train routing and timetabling problem that allows a train to occasionally switch to the opposite track when it is not occupied, which we define it as switchable scheduling rule. The layouts of stations are taken into account in the proposed mathematical model to avoid head-on and rear-end collisions in stations. In this paper, train timetable could be scheduled by three different scheduling rules, i.e., no switchable scheduling rule (No-SSR) which allows trains switching track neither at stations and segments, incomplete switchable scheduling rule (In-SSR) which allows trains switching track at stations but not at segments, and complete switchable scheduling rule (Co-SSR) which allows trains switching track both at stations and segments. Numerical experiments are carried out on a small-scale railway corridor and a large-scale railway corridor based on Beijing–Shanghai high-speed railway (HSR) corridor respectively. The results of case studies indicate that Co-SSR outperforms the other two scheduling rules. It is also found that the proposed model can improve train operational efficiency.     

Spatial decision support system for hazardous material truck routing

Shipping hazardous material (hazmat) places the public at risk. People who live or work near roads commonly traveled by hazmat trucks endure the greatest risk. Careful selection of roads used for a hazmat shipment can reduce the population at risk. On the other hand, a least time route will often consist of urban interstate, thus placing many people in harms way. Route selection is therefore the process of resolving the conflict between population at risk and efficiency considerations. To assist in resolving this conflict, a working spatial decision support system (SDSS) called Hazmat Path is developed. The proposed hazmat routing SDSS overcomes three significant challenges, namely handling a realistic network, offering sophisticated route generating heuristics and functioning on a desktop personal computer. The paper discusses creative approaches to data manipulation, data and solution visualization, user interfaces, and optimization heuristics implemented in Hazmat Path to meet these challenges.     

Robust supply vessel routing and scheduling

We solve the problem of tactical supply vessel planning arising in the upstream offshore petroleum logistics. Supply vessels deliver all the necessary materials and equipment to offshore installations from an onshore supply base according to a delivery schedule. The planning of supply vessels should be done so that their number is minimized and at the same time provide a reliable flow of supplies from the base. The execution of a weekly sailing plan is affected by weather conditions, especially in winter time. Harsh weather conditions increase the number of vessels required to perform the operations as well as the service times at the installations, and thus disrupt the schedule, leading to additional costs and reduced service level. We present a methodology for robust supply vessel planning enabling a trade-off analysis to be made between the schedules’ service level and vessels’ cost. The methodology involves the generation of multiple vessel schedules with different level of robustness using an adaptive large neighbourhood search metaheuristic and a subsequent discrete event simulation procedure for the assessment of the service level. To control the level of robustness we developed a concept of slacks and incorporated it into the metaheuristic algorithm.     

Research perspectives in vehicle routing and scheduling

The problem of vehicle routing and scheduling has been a popular research subject, yet much of the research has focused on developing methods that are accurate and computationally efficient but that are generally of limited scope. This article classifies these methodologies and appraises each class. Perhaps more important, the article identifies those restrictions and extensions that should be incorporated into a generalized vehicle routing and scheduling methodology and, therefore, points the direction for future research.     

Multi-objective optimization of train routing problem combined with train scheduling on a high-speed railway network

Based on train scheduling, this paper puts forward a multi-objective optimization model for train routing on high-speed railway network, which can offer an important reference for train plan to provide a better service. The model does not only consider the average travel time of trains, but also take the energy consumption and the user satisfaction into account. Based on this model, an improved GA is designed to solve the train routing problem. The simulation results demonstrate that the accurate algorithm is suitable for a small-scale network, while the improved genetic algorithm based on train control (GATC) applies to a large-scale network. Finally, a sensitivity analysis of the parameters is performed to obtain the ideal parameters; a perturbation analysis shows that the proposed method can quickly handle the train disturbance.     

Time-dependent fuzzy random location-scheduling programming for hazardous materials transportation

The tremendous use of hazardous materials has promoted the economic development, which also brings about a growing risk causing a widespread concern. In this work, we consider a location-scheduling problem on hazardous materials transportation under the assumption that transportation risks are time-dependent fuzzy random variables. First, we formulate a scheduling optimization model and design a fuzzy random simulation based genetic algorithm to optimize the departure time and dwell times for each depot–customer pair. Then we establish an expected value model and design a modified particle swarm optimization algorithm to minimize the en route risks and site risks. Finally, numerical examples are given to illustrate the effectiveness of the proposed models and algorithms.     

Heuristic search for the coupled runway sequencing and taxiway routing problem

This paper presents the first local search heuristic for the coupled runway sequencing (arrival & departure) and taxiway routing problems, based on the receding horizon (RH) scheme that takes into account the dynamic nature of the problem. As test case, we use Manchester Airport, the third busiest airport in the UK. From the ground movement perspective, the airport layout requires that departing aircraft taxi across the arrivals runway. This makes it impossible to separate arrival from departure sequencing in practice. Operationally, interactions between aircraft on the taxiways could prevent aircraft from taking off from, or landing on, runways during the slots assigned to them by an algorithm optimizing runway use alone. We thus consider the interactions between arrival and departure aircraft on the airport surface. Compared to sequentially optimized solutions, the results obtained with our approach indicate a significant decrease in the taxiway routing delay, with generally no loss in performance in terms of the sequencing delay for a regular day of operations. Another benefit of such a simultaneous optimization approach is the possibility of holding aircraft at the stands for longer, without the engines running. This significantly reduces the fuel burn, as well as bottlenecks and traffic congestion during peak hours that are often the cause of flight delays due to the limited amount of airport surface space available. Given that the maximum computing time per horizon is around 95 s, real-time operation might be practical with increased computing power.     

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.     

A lamda-optimal based heuristic for the berth scheduling problem

Berth scheduling aims to optimally schedule vessels to berthing areas along a quay and is a complex optimization problem. In this paper we propose a lamda-optimal based heuristic as a resolution approach for the discrete space berth scheduling problem. The proposed heuristic can also be applied to validate optimality, in the case where other (meta)heuristics are applied as resolution approaches. A second internal Genetic Algorithms based heuristic is also proposed to reduce the computational time required for medium to large scale instances. Numerical experiments performed show that the proposed heuristic is adequate to produce near-optimal results within acceptable computational times.     

Automation of paratransit reservation,routing, and scheduling

Santa Clara County, California experienced a sharp growth in demand‐responsive paratransit ridership for individuals with disabilities, as a result of the passage of the 1990 Americans With Disabilities Act (ADA). This paper describes an automated paratransit system for the ADA‐type paratransit operation implemented in Santa Clara County. It automated paratransit reservation, scheduling, and routing functions. The key components of this system were a digital geographic database (DGD) and an automated trip scheduling system (ATSS). Empirical evidence after one year of operation indicates numerous benefits of this automation. There were significant reductions in the paratransit operating costs and an increase in the percent shared rides. The savings in operating costs far exceeded the annualized capital cost of automation. A user survey indicates that these improvements were achieved without degradation to service quality such as vehicle on‐time performance, invehicle travel times, vehicle response to open return, and ride comfort.     

A model and optimization-based heuristic for the operational aircraft maintenance routing problem

This paper investigates the Operational Aircraft Maintenance Routing Problem (OAMRP). Given a set of flights for a specific homogeneous fleet type, this short-term planning problem requires building feasible aircraft routes that cover each flight exactly once and that satisfy maintenance requirements. Basically, these requirements enforce an aircraft to undergo a planned maintenance at a specified station before accumulating a maximum number of flying hours. This stage is significant to airline companies as it directly impacts the fleet availability, safety, and profitability. The contribution of this paper is twofold. First, we elucidate the complexity status of the OAMRP and we propose an exact mixed-integer programming model that includes a polynomial number of variables and constraints. Furthermore, we propose a graph reduction procedure and valid inequalities that aim at improving the model solvability. Second, we propose a very large-scale neighborhood search algorithm along with a procedure for computing tight lower bounds. We present the results of extensive computational experiments that were carried out on real-world flight networks and attest to the efficacy of the proposed exact and heuristic approaches. In particular, we provide evidence that the exact model delivers optimal solutions for instances with up to 354 flights and 8 aircraft, and that the heuristic approach consistently delivers high-quality solutions while requiring short CPU times.     

Robust weekly aircraft maintenance routing problem and the extension to the tail assignment problem

In this paper, we study two closely related airline planning problems: the robust weekly aircraft maintenance routing problem (RWAMRP) and the tail assignment problem (TAP). In real life operations, the RWAMRP solution is used in tactical planning whereas the TAP solution is implemented in operational planning. The main objective of these two problems is to minimize the total expected propagated delay (EPD) of the aircraft routes. To formulate the RWAMRP, we propose a novel weekly line-of-flights (LOF) network model that can handle complex and nonlinear cost functions of EPD. Because the number of LOFs grows exponentially with the number of flights to be scheduled, we propose a two-stage column generation approach to efficiently solve large-scale real-life RWAMRPs. Because the EPD of an LOF is highly nonlinear and can be very time-consuming to accurately compute, we propose three lower bounds on the EPD to solve the pricing subproblem of the column generation. Our approach is tested on eight real-life test instances. The computational results show that the proposed approach provides very tight LP relaxation (within 0.6% of optimal solutions) and solves the test case with more than 6000 flights per week in less than three hours. We also investigate the solutions obtained by our approach over 500 simulated realizations. The simulation results demonstrate that, in all eight test instances, our solutions result in less EPDs than those obtained from traditional methods. We then extend our model and solution approach to solve realistically simulated TAP instances.     

A branch-and-price approach for solving the train unit scheduling problem

We propose a branch-and-price approach for solving the integer multicommodity flow model for the network-level train unit scheduling problem (TUSP). Given a train operator’s fixed timetable and a fleet of train units of different types, the TUSP aims at determining an assignment plan such that each train trip in the timetable is appropriately covered by a single or coupled train units. The TUSP is challenging due to its complex nature. Our branch-and-price approach includes a branching system with multiple branching rules for satisfying real-world requirements that are difficult to realize by linear constraints, such as unit type coupling compatibility relations and locations banned for coupling/decoupling. The approach also benefits from an adaptive node selection method, a column inheritance strategy and a feature of estimated upper bounds with node reservation functions. The branch-and-price solver designed for TUSP is capable of handling instances of up to about 500 train trips. Computational experiments were conducted based on real-world problem instances from First ScotRail. The results are satisfied by rail practitioners and are generally competitive or better than the manual ones.     

A column generation algorithm for the bus driver scheduling problem

Bus driver scheduling aims to find the minimum number of bus drivers to cover a published timetable of a bus company. When scheduling bus drivers, contractual working rules must be enforced, thus complicating the problem. In this research, we develop a column generation algorithm that decomposes this complicated problem into a master problem and a series of pricing subproblems. The master problem selects optimal duties from a set of known feasible duties, and the pricing subproblem augments the feasible duty set to improve the solution obtained in the master problem. The proposed algorithm is empirically applied to the realistic problems of several bus companies. The numerical results show that the proposed column generation algorithm can solve real‐world problems and obtain bus driver schedules that are better than those developed and used by the bus companies. Copyright © 2016 John Wiley & Sons, Ltd.     

Methodological aspects for modeling the environmental risk of transporting hazardous materials by road

The main objective of this paper is to establish the procedures necessary to the development of a model for the environmental risk assessment of accidents involving Transporting Hazardous Materials by Road (THMR). Quantifying the environmental risk is useful in identifying areas with a high risk of accidents, which can be later discarded as main routes; orienting efficient emergency response operations; and assessing policies aimed at reducing these risks. Taking this into consideration, this study endeavors to identify the methodological aspects make possible the assessment of the impacts that arise from accidents involving the transportation of hazardous materials by road and to implement such methodological aspects in a Geographic Information System (GIS).     

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.     

An algorithm for the combined distribution and assignment problem

Much interest has recently been shown in the combination of the distribution and assignment models. In this paper we adopt a generalized Benders' decomposition to solve this combined problem for a system optimized assignment with linear link costs and explicit capacity constraints on link flows. The master problem which is generated is used to show that the combined problem can be viewed as a modified distribution problem, of gravity form, with a minimax instead of a linear objective function. An algorithm for solving the master problem is discussed, and some computational results presented.     

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.