A case study of Beijing bus crew scheduling: a variable neighborhood‐based approach

Crew scheduling for bus drivers in large bus agencies is known to be a time‐consuming and cumbersome problem in transit operations planning. This paper investigates a new meta‐heuristics approach for solving real‐world bus‐driver scheduling problems. The drivers' work is represented as a series of successive pieces of work with time windows, and a variable neighborhood search (VNS) algorithm is employed to solve the problem of driver scheduling. Examination of the modeling procedure developed is performed by a case study of two depots of the Beijing Public Transport Group, one of the largest transit companies in the world. The results show that a VNS‐based algorithm can reduce total driver costs by up to 18.1%, implying that the VNS algorithm may be regarded as a good optimization technique to solve the bus‐driver scheduling problem. Copyright © 2015 John Wiley & Sons, Ltd.     

A dynamic empty equipment and crew allocation model for long-haul networks

This research develops a realistic and efficient operational model to optimize empty equipment and crew movements in long-haul trucking networks with consolidation, where returning drivers home within a reasonable amount of time is an important issue. The problem can be stated as follows. On a network of consolidation centers, demand is expressed as a set of trailer-loads that need to be moved between each pair of consolidation centers in each time period and the objective is to optimize trailer, tractor and driver movements while ensuring that drivers return home within a pre-determined period of time. In this paper, a dynamic integer programming model is developed and an efficient approximate solution method is proposed, which involves column generation and branch-and-bound. The algorithm switches from a combination of network and primal simplex to dual simplex to overcome the degeneracy problem, which is very common for dynamic networks. This novel approach enables solving large problems with many intervals. We solved problems with up to 30 nodes and 48 periods successfully by using real data provided by a less-than-truckload company, and by generating statistical forecasts based on the real data.     

Relaxation approaches to large scale bus driver scheduling problems

The bus driver scheduling (BDS) problem in a transit company consists of establishing, at minimum cost, a list of work-days in which a driver is assigned to each bus in the given time-table and all clauses of the union contract are respected. In this paper we present a general mathematical programming formulation for the BDS problem. Because, in general, the problem is too large to be solved directly, we introduce a relation of the problem and three different solution approaches. Computational results obtained on real life problems indicate that mathematical programming techniques can solve the BDS problem efficiently.     

Bus maintenance systems and maintenance scheduling: model formulations and solutions

This paper deals with the problem of scheduling bus maintenance activities. The scheduling of maintenance activities is an important component in bus transit operations planning process. The other components include network route design, setting timetables, scheduling vehicles, and assignment of drivers. This paper presents a mathematical programming approach to the problem. This approach takes as input a given daily operating schedule for all buses assigned to a depot along with available maintenance resources. It, then, attempts to design daily inspection and maintenance schedules for the buses that are due for inspection so as to minimize the interruptions in the daily bus operating schedule, and maximize the utilization of the maintenance facilities. Three integer programming formulations are presented and different properties of the problem are discussed. Several heuristic methods are presented and tested. Some of these procedures produce very close to optimal solutions very efficiently. In some cases, the computational times required to obtain these solutions are less than 1% of the computational time required for the conventional branch and bound algorithm. Several small examples are offered and the computational results of solving the problem for an actual, 181-bus transit property are reported.     

Mitigation of disruptions in public transit by Bee Colony Optimization

Dispatchers in many public transit companies face the daily problem of assigning available buses to bus routes under conditions of bus shortages. In addition to this, weather conditions, crew absenteeism, traffic accidents, traffic congestion and other factors lead to disturbances of the planned schedule. We propose the Bee Colony Optimization (BCO) algorithm for mitigation of bus schedule disturbances. The developed model takes care of interests of the transit operator and passengers. The model reassigns available buses to bus routes and, if it is allowed, the model simultaneously changes the transportation network topology (it shortens some of the planned bus routes) and reassigns available buses to a new set of bus routes. The model is tested on the network of Rivera (Uruguay). Results obtained show that the proposed algorithm can significantly mitigate disruptions.     

A bi-level programming for bus lane network design

This paper proposes a bi-level programming model to solve the design problem for bus lane distribution in multi-modal transport networks. The upper level model aims at minimizing the average travel time of travelers, as well as minimizing the difference of passengers’ comfort among all the bus lines by optimizing bus frequencies. The lower level model is a multi-modal transport network equilibrium model for the joint modal split/traffic assignment problem. The column generation algorithm, the branch-and-bound algorithm and the method of successive averages are comprehensively applied in this paper for the solution of the bi-level model. A simple numerical test and an empirical test based on Dalian economic zone are employed to validate the proposed model. The results show that the bi-level model performs well with regard to the objective of reducing travel time costs for all travelers and balancing transit service level among all bus lines.     

The effects of eco-driving motivation,knowledge and reward intervention on fuel efficiency

Every year, bus companies consume millions of litres of fuel, and their fuel costs often exceed millions of US dollars. These companies have an obvious interest in reducing their fuel consumption. One way to encourage drivers to engage in eco-driving behaviours, as well as their related beliefs, is to use a monetary reward system. The aim of this study was to explore the incentive effects of such a reward system to encourage better driving behaviours among bus drivers. This study collected fuel-efficiency data before and after the implementation of a reward system. Furthermore, to study the effects that the system had on driver behaviours, this study adopted the theory of Motivation–Opportunity–Ability (MOA) to construct the regression model. The results for the average fuel consumption efficiency for the buses before and after the reward system was introduced showed an improvement of more than 10% and thus a reduction in carbon emissions.     

Eco-driving training of professional bus drivers – Does it work?

The drive to reduce fuel consumption and greenhouse gas emissions is one shared by both businesses and governments. Although many businesses in the European Union undertake interventions, such as driver training, there is relatively little research which has tested the efficacy of this approach and that which does exist has methodological limitations. One emerging technology employed to deliver eco-driving training is driver training using a simulator. The present study investigated whether bus drivers trained in eco-driving techniques were able to implement this learning in a simulator and whether this training would also transfer into the workplace. A total of 29 bus drivers attended an all-day eco-driving course and their driving was tested using a simulator both before and after the course. A further 18 bus drivers comprised the control group, and they attended first aid courses as well as completing the same simulator drives (before-after training). The bus drivers who were given the eco-driving training significantly improved fuel economy figures in the simulator, while there was no change in fuel economy for the control group. Actual fuel economy figures were also provided by the bus companies immediately before the training, immediately after the training and six months after the training. As expected there were no significant changes in fuel economy for the control group. However, fuel economy for the treatment group improved significantly immediately after the eco-driving training (11.6%) and this improvement was even larger six months after the training (16.9%). This study shows that simulator-based training in eco-driving techniques has the potential to significantly reduce fuel consumption and greenhouse gas emissions in the road transport sector.     

Heuristic approaches for solving large-scale bus transit vehicle scheduling problem with route time constraints

This paper presents new models for multiple depot vehicle scheduling problem (MDVS) and multiple depot vehicle scheduling problem with route time constraints (MDVSRTC). The route time constraints are added to the MDVS problem to account for the real world operational restrictions such as fuel consumption. Compared to existing formulations, this formulation decreases the size of the problem by about 40% without eliminating any feasible solution. It also presents an exact and two heuristic solution procedures for solving the MDVSRTC problem. Although these methods can be used to solve medium size problems in reasonable time, real world applications in large cities require that the MDVSRTC problem size be reduced. Two techniques are proposed to decrease the size of the real world problems. For real-world application, the problem of bus transit vehicle scheduling at the mass transit administration (MTA) in Baltimore is studied. The final results of model implementation are compared to the MTA's schedules in January 1998. The comparison indicates that, the proposed model improves upon the MTA schedules in all respects. The improvements are 7.9% in the number of vehicles, 4.66% in the operational time and 5.77% in the total cost.     

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.     

What drives the drivers? Predicting turnover intentions in the Belgian bus and coach industry

The bus industry is characterized by demanding jobs and high turnover rates. In this study we gather essential insights that can help companies and industry-level policy makers increase the attractiveness of the profession and design effective retention policies. We compare the factors that induce Belgian drivers to leave their current organization with those inducing them to leave the industry. Key factors increasing the likelihood to consider quitting the company are a negative work-life balance, a lack of social support and a temporary contract. Dominant factors to consider quitting the bus driver profession are a lack of fulfillment, a demanding job environment and a negative work-life balance.     

Vehicle routing problem and driver behaviour: a review and framework for analysis

Vehicle routing problems (VRPs) whose typical objective is to minimise total travel costs over a tour have evolved over the years with objectives ranging from minimising travel times and distances to minimising pollution and fuel consumption. However, driver behaviour continues to be neglected while planning for vehicle routes. Factors such as traffic congestion levels, monotonous drives and fatigue have an impact on the behaviour of drivers, which in turn might affect their speed-choice and route-choice behaviours. The behaviour of drivers and their subsequent decision-making owing to these factors impact the revenue of transport companies and could lead to huge losses in extreme cases. There have been studies on the behaviour of drivers in isolation, without inclusion of the objectives and constraints of the traditional routing problem. This paper presents a review of existing models of VRP, planner behaviour models in the VRP context and driver behaviour models and provides a motivation to integrate these models in a stochastic traffic environment to produce practical, economic and driver-friendly logistics solutions. The paper provides valuable insights on the relevance of behavioural issues in logistics and highlights the modelling implications of incorporating planner and driver behaviour in the framework of routing problems.     

道路客运小件快运车辆路径和调度研究

制约小件运输发展的瓶颈之一是站到站运输与客户门到门需求之间的矛盾,目前道路客运企业正大力发展门到门的取送货业务,但缺少一套切实可行的取送货运输组织调度方案,基于此,文章建立了考虑客户时效性需求的车辆路径调度数学模型并设计了一种改进的遗传算法进行求解。通过实例证明该算法可以求得满意解,为道路客运企业发展小件快运的"最后一公里"取送货服务提供运输组织调度方案参考。     

Privacy-preserving MaaS fleet management

On-demand traffic fleet optimization requires operating Mobility as a Service (MaaS) companies such as Uber, Lyft to locally match the offer of available vehicles with their expected number of requests referred to as demand (as well as to take into account other constraints such as driver’s schedules and preferences). In the present article, we show that this problem can be encoded into a Constrained Integer Quadratic Program (CIQP) with block independent constraints that can then be relaxed in the form of a convex optimization program. We leverage this particular structure to yield a scalable distributed optimization algorithm corresponding to computing a gradient ascent in a dual space. This new framework does not require the drivers to share their availabilities with the operating company (as opposed to standard practice in today’s mobility as a service companies). The resulting parallel algorithm can run on a distributed smartphone based platform.     

Market mechanism design for profitable on-demand transport services

On-demand transport services in the form of dial-a-ride and taxis are crucial parts of the transport infrastructure in all major cities. However, not all on-demand transport services are equal: not-for-profit dial-a-ride services with coordinated drivers significantly differ from profit-motivated taxi services with uncoordinated drivers. In fact, there are two key threads of work on efficient scheduling, routing, and pricing for passengers: dial-a-ride services; and taxi services. Unfortunately, there has been only limited development of algorithms for joint optimization of scheduling, routing, and pricing; largely due to the widespread assumption of fixed pricing. In this paper, we introduce another thread: profit-motivated on-demand transport services with coordinated drivers. To maximize provider profits and the efficiency of the service, we propose a new market mechanism for this new thread of on-demand transport services, where passengers negotiate with the service provider. In contrast to previous work, our mechanism jointly optimizes scheduling, routing, and pricing. Ultimately, we demonstrate that our approach can lead to higher profits and reduced passenger prices, compared with standard fixed price approaches, while also improving efficiency.     

A multi-period dial-a-ride problem with driver consistency

Dial-a-ride services provide disabled and elderly people with a personalized mode of transportation to preserve their mobility. Typically, several users with different pickup and dropoff locations are transported on a vehicle simultaneously. The focus in dial-a-ride problems (DARPs) is mainly on minimizing routing cost. Service quality has been taken into account in the models by imposing time windows and limiting the maximum ride time of each user. We extend the classical DARP by an additional feature of service quality referred to as driver consistency. Customers of dial-a-ride services are often sensitive to changes in their daily routine. This aspect includes the person who is providing the transportation service, i.e., the driver of the vehicle. Our problem, called the driver consistent dial-a-ride problem (DC-DARP), considers driver consistency by bounding the maximum number of different drivers that transport a user over a multi-period planning horizon.We propose different formulations of the problem and examine their efficiency when applied in a Branch-and-Cut fashion. Additionally, we develop a large neighborhood search algorithm that generates near-optimal solutions in a short amount of time.Over 1000 instances are generated with close reference to real world scenarios. Extensive computational experiments are conducted in order to assess the quality of the solution approaches and to provide insights into the new problem. Results reveal that the cost of offering driver consistency varies greatly in magnitude. Depending on the instance, the cost of assigning one driver to each user can be up to 27.98% higher compared to a low-cost solution. However, routing cost increases by not more than 5.80% if users are transported by at least two drivers.     

Vehicle monitoring for driver training in bus companies – Application in two case studies in Portugal

We examine the strategies of modifying drive behavior adopted by two bus companies operating in the Lisbon Metropolitan Area to minimize fuel consumption and associated CO₂ emissions. Rodoviária de Lisboa uses a commercial tool for monitoring buses during regular work, with data collected based on events representing undesired behavior that was subsequently used as the basis for classroom training of drivers. Barraqueiro Transportes adopted a vehicle monitoring system capable of processing information during operation giving real time driver feedback on energy, comfort and safety indicators. Both systems produced fuel economies, although to differing degrees.     

Evolutionary crew scheduling with adaptive chromosomes

This paper presents an adaptive evolutionary approach incorporating a hybrid genetic algorithm (GA) for public transport crew scheduling problems, which are well-known to be NP-hard. To ensure the search efficiency, a suitable chromosome representation has to be determined first. Unlike a canonical GA for crew scheduling where the chromosome length is fixed, the chromosome length in the proposed approach may vary adaptively during the iterative process, and its initial value is elaborately designated as the lower bound of the number of shifts to be used in an unachievable optimal solution. Next, the hybrid GA with such a short chromosome length is employed to find a feasible schedule. During the GA process, the adaptation on chromosome lengths is achieved by genetic operations of crossover and mutation with removal and replenishment strategies aided by a simple greedy algorithm. If a feasible schedule cannot be found when the GA’s termination condition is met, the GA will restart with one more gene added. The above process is repeated until a feasible solution is found. Computational experiments based on 11 real-world crew scheduling problems in China show that, compared to a fuzzy GA known to be well performed for crew scheduling, better solutions are found for all the testing problems. Moreover, the algorithm works fast, has achieved results close to the lower bounds obtained by a standard linear programming solver in terms of the number of shifts, and has much potential for future developments.     

Optimization of periodic crew schedules with application of column generation method

We present an alternative approach to the problem of periodic crew scheduling. We introduce the concept of frames which leads us to a modeling approach which suits well the current practice of the majority of European railway operators. It results in a model facilitating column generation techniques resulting in a Dantzig-Wolfe type decomposition, and thus suitable for a parallel implementation in a high-performance computing environment. We exploit the properties of network flow models to avoid several additional integer constraints. We compare two approaches to solve the problem. The first approach consists of solving the original problem by single model. The second approach is our step-by-step column generation. The comparison is based on our implementation which we describe in detail along with its application to certain benchmark instances. The benchmarks originate in real or close-to-realistic problems from railway systems in Slovakia and Hungary. The case studies demonstrate that our model is well-suited for real-life applications.     

An online speed profile generation approach for efficient airport ground movement

The precise guidance and control of taxiing aircraft based on four-dimensional trajectories (4DTs) has been recognised as a promising means to ensure safe and efficient airport ground movement in the context of ever growing air traffic demand. In this paper, a systematic approach for online speed profile generation is proposed. The aim is to generate fuel-efficient speed profiles respecting the timing constraints imposed by routing and scheduling, which ensures conflict-free movement of aircraft in the planning stage. The problem is first formulated as a nonlinear optimisation model, which uses a more flexible edge-based speed profile definition. A decomposed solution approach (following the framework of matheuristic) is then proposed to generate feasible speed profiles in real time. The decomposed solution approach reduces the nonlinear optimisation model into three tractable constituent problems. The control point arrival time allocation problem is solved using linear programming. The control point speed allocation problem is solved using particle swarm optimisation. And the complete speed profile between control points is determined using enumeration. Finally, improved speed profiles are generated through further optimisation upon the feasible speed profiles. The effectiveness and advantages of the proposed approach are validated using datasets of real-world airports.