Driver Scheduling Problem Research Articles

Investigating Large Neighbourhood Search for Bus Driver Scheduling

The Bus Driver Scheduling Problem (BDSP) is a combinatorial optimisation problem with high practical relevance. The aim is to assign bus drivers to predetermined routes while minimising a specified objective function that considers operating costs as well as employee satisfaction. Since we must satisfy several rules from a collective agreement and European regulations, the BDSP is highly constrained. Hence, using exact methods to solve large real-life-based instances is computationally too expensive, while heuristic methods still have a considerable gap to the optimum. Our paper presents a Large Neighbourhood Search (LNS) approach to solve the BDSP. We propose several novel destroy operators and an approach using column generation to repair the sub-problem. We analyse the impact of the destroy and repair operators and investigate various possibilities to select them, including adaptivity. The proposed approach improves all the upper bounds for larger instances that exact methods cannot solve, as well as for some mid-sized instances, and outperforms existing heuristic approaches for this problem on all benchmark instances.

A label-setting algorithm for the truck driver scheduling problem in accordance with European Community social legislation

In this paper, a label-setting algorithm is proposed in order to efficiently solve the weekly Truck Driver Scheduling Problem (TDSP), which can be seen as a single-machine problem that minimizes the completion time of a fixed sequence of jobs with release and due times and break periods. A focus is made on the night working rule that has only partially been considered in the literature. In the wide literature dedicated to Vehicle Routing Problems, some published heuristics and exact algorithms include constraints related to break/rest periods. But the night working rule defined by the European Community Social Legislation is only considered in some simplified and sub-optimal versions. This constraint is of interest, since it has a direct impact on the practical applicability of routes. Moreover, from a scheduling point of view, the night working rule enforces minimum and maximum time lag constraints, which makes challenging the development of an efficient solution algorithm. The method is benchmarked with a mixed integer linear programming model. Computational experiments show the efficiency of the proposed methods and the effect of the night working constraint on the feasibility of the schedules.

A Time-Space Network-Based Optimization Method for Scheduling Depot Drivers

The driver scheduling problem at Chinese electric multiple-unit train depots becomes more and more difficult in practice and is studied in very little research. This paper focuses on defining, modeling, and solving the depot driver scheduling problem which can determine driver size and driver schedule simultaneously. To solve this problem, we first construct a time-space network based on which we formulate the problem as a minimum-cost multi-commodity network flow problem. We then develop a Lagrangian relaxation heuristic to solve this network flow problem, where the upper bound heuristic is a two-phase method consisting of a greedy heuristic and a local search method. We conduct a computational study to test the effectiveness of our Lagrangian relaxation heuristic. The computational results also report the significance of the ratio of driver size to task size in the depot.

Using state-space shortest-path heuristics to solve the long-haul point-to-point vehicle routing and driver scheduling problem subject to hours-of-service regulatory constraints

Using state-space shortest-path heuristics to solve the long-haul point-to-point vehicle routing and driver scheduling problem subject to hours-of-service regulatory constraints

A column generation approach for the driver scheduling problem with staff cars

Given a set of timetabled bus trips, transport companies are faced with the challenge of finding a feasible driver schedule that covers all trips and abides by various labor union regulations. The regulations are primarily concerned with providing sufficient breaks for the drivers during the day. Practical limitations in the city network enforce drivers to travel by cars between bus stops to have breaks. Transport companies have a limited number of cars, known as staff cars, which have to be returned to their respective depots at the end of the day. The simultaneous scheduling of drivers and staff cars for the drivers is known as the driver scheduling problem with staff cars (DSPSC). It is estimated that the DSPSC accounts for 60% of a bus company’s operational expense, and this paper proposes a column generation approach that attempts to minimize operational expense. The column-generation framework iterates between a master problem, a subproblem for generating driver variables and a subproblem for generating staff car variables. The subproblem related to the drivers is formulated as a resource constrained shortest path problem, which is solved by a dynamic programming approach. Several heuristic branching strategies are explored to find integer solutions. The proposed methodology is tested on eight real-life instances from seven Northern European bus companies. A comparison with a state-of-the-art mixed integer programming (MIP) solver and an adaptive large neighborhood search (ALNS) heuristic indicate that the column generation approach provides improved solutions for six instances and the average improvement is 1.45%.

Scheduling truck drivers with interdependent routes under European Union regulations

When transporting goods, truck drivers may have to perform load transfers between two vehicles at cross-dock or transfer locations. These transfers create interdependencies between the routes of different truck drivers and require careful temporal synchronization. The situation becomes even more complicated when driver schedules must comply with customer time windows, working periods and regulatory resting requirements. Although the scheduling of hours of service for truck drivers is a well-known problem, existing algorithms cannot cope with interdependent routes. We introduce the Truck Driver Scheduling Problem with Interdependent Routes to successfully accommodate this real-world characteristic. This paper proposes a mathematical model and a label propagation algorithm to solve this new problem under the regulations of the European Union. Experiments indicate that the algorithm can quickly schedule a large number of interdependent routes and outperforms a mathematical programming approach. The algorithm produces valid schedules for multiple drivers and thus becomes a foundation for future vehicle routing algorithms that address interdependent routes and hours of service regulations.

Branch and Price for Bus Driver Scheduling with Complex Break Constraints

This paper presents a Branch and Price approach for a real-life Bus Driver Scheduling problem with a complex set of break constraints. The column generation uses a set partitioning model as master problem and a resource constrained shortest path problem as subproblem. Due to the complex constraints, the branch and price algorithm adopts several novel ideas to improve the column generation in the presence of a high-dimensional subproblem, including exponential arc throttling and a dedicated two-stage dominance algorithm. Evaluation on a publicly available set of benchmark instances shows that the approach provides the first provably optimal solutions for small instances, improving best-known solutions or proving them optimal for 48 out of 50 instances, and yielding an optimality gap of less than 1% for more than half the instances.

Vehicle and reliable driver scheduling for public bus transportation systems

We propose the bus vehicle and reliable driver scheduling problem that is an integrated approach for the vehicle and the crew scheduling problems considering driver’s reliability information to reduce the number of no-covered trips along the day and thus improve the user’s satisfaction. An exact constraint programming model is proposed and compared with a variable neighborhood search that incorporates the driver’s reliability and the trip’s importance. The obtained trip-vehicle-driver assignments are evaluated on many scenarios with a Monte Carlo method to simulate the driver’s absenteeism. Experimental results on randomly generated instances based on a real case study show our methodologies’ efficiency and the enormous gains in covered trips when the drivers’ reliability is considered.

Solving Large Real-Life Bus Driver Scheduling Problems with Complex Break Constraints

When scheduling drivers for public transport, in addition to covering the demand and dealing with the spatial dimension, a range of legal requirements, collective agreements and company policies need to be respected. The level of concentration required while driving leads to strict rules for break assignments. This results in a complex problem where creating cost-efficient and employee-friendly schedules is challenging. This paper deals with bus driver scheduling using the rules of the Austrian collective agreement for private omnibus providers. The contributions are the formalization of the complex Austrian rules for bus drivers, a new set of publicly available instances based on the characteristics of real-life instances, and a metaheuristic solution approach for the problem. The algorithm was able to significantly improve the solutions of real-life instances and is evaluated on the generated instances. Further we provide insight in the necessity of objectives for employee satisfaction and their effects. Our method can even be successfully applied to improve results on a problem with very different constraints from Brasil.

Bus driver scheduling enhancement: a derandomizing approach for uncertain bus trip times

The bus driver scheduling problems aim to optimally deploy drivers to fulfil published timetables for bus services subject to drivers’ contractual working rules. In this study, we first develop an integer linear programming model for a practical driver scheduling problem. We proceed to formulate another integer linear programming model for the driver scheduling enhancement to incorporate with uncertain bus travel times, which are addressed by an effective derandomizing approach. Moreover, the lower and upper bounds of the developed models are investigated by using the Lagrangian problems with which the solution quality can be evaluated. To assess the efficiency and applicability of the developed models, we conduct a case study based on historical operational data of the bus route #95 in Singapore. Finally, we perform a necessary sensitivity analysis of the bus fleet size and driver workload on the bus driver scheduling problems to identify some valuable managerial insights.

Bidirectional labeling for solving vehicle routing and truck driver scheduling problems

This paper studies the vehicle routing and truck driver scheduling problem where routes and schedules must comply with hours of service regulations for truck drivers. It presents a backward labeling method for generating feasible schedules and shows how the labels generated with the backward method can be combined with labels generated by a forward labeling method. The bidirectional labeling is embedded into a branch-and-price-and-cut approach and evaluated for hours of service regulations in the United States and the European Union. Computational experiments show that the resulting bidirectional branch-and-price-and-cut approach is significantly faster than unidirectional counterparts and previous approaches.

On a multi-trip vehicle routing problem with time windows integrating European and French driver regulations

In the European Union, truck drivers must comply with Regulation (EC) No 561/2006, which provides a set of rules on the daily or weekly working time and on break or rest periods after specific working times. Truck drivers can be back to the depot much earlier than the end of their working period, and be able to perform other trips. The resulting problem is a Multi-Trip Vehicle Routing Problem with Time Windows, where truck drivers have the possibility to accomplish, during their time horizon, more than one trip, combined with a Truck Driver Scheduling Problem. It aimed to find and assign a set of routes to a fleet of vehicles allowing each customer to be visited within its given time window, and the accumulated load to be delivered (or collected) not exceeding the capacity of the vehicle. Each truck driver must comply with applicable hours of service regulations, and the objective is to minimize total transportation cost. To solve this problem, we have developed a hybrid method composed of a genetic algorithm and a local neighborhood search. Experiments have been conducted on instances from the literature and real-life cases from SYSTRANS, a specialized French software company.

Bus and driver scheduling with mealtime windows for a single public bus route

This study deals with the bus & driver scheduling problems with mealtime windows for a single public transport bus route. Firstly, we develop three explicit Integer Linear Programming (ILP) models to formulate: the bus driver scheduling, bus & driver scheduling, and bus & driver scheduling with mealtime windows, respectively. These ILP models enable bus operators to solve their bus & driver scheduling problems by directly invoking an available optimization solver such as IBM ILOG CPLEX. However, our numerical experiments do not show remarkable improvements, as CPLEX takes more than 12, 17, and 35 h respectively to reduce the optimality gap to at most 0.5% for solving the above three models in an over 12-hour bus & driver scheduling problem. To improve the computational efficiency, we develop a valid inequality approach that can generate valid cuts incorporating with the CPLEX. An investigation into the valid inequality approach proves its high computational efficiency. In addition, we develop a self-adaptive search method for determining the upper and lower bounds of driver group and bus fleet sizes. Finally, we test our models and approaches on a real round-trip bus route. The results indicate that compared with the only use of CPLEX to solve the above three models, the valid inequality approach can address large-scale instances in a reasonable CPU time.

Constrained Self-Adaptive Harmony Search Algorithm with 2-opt Swapping for Driver Scheduling Problem of University Shuttle Bus

A constrained self-adaptive harmony search algorithm (CSAHS) with 2-opt swapping (CSAHS-2opt) for driver scheduling problem of university shuttle bus (DSPUSB) was proposed in this study. In generating a schedule, there are some constraints that should be catered to obtain an optimum result. In DSPUSB, fairness of task distribution among drivers is one of the main issues that are very crucial and can affect the performance and quality of services. Therefore, to maximise the fairness, the violation of soft constraints for DSPUSB including shift and route should be minimised. CSAHS with 2-opt swapping was proposed focusing on minimising soft constraint violation. In standard harmony search (HS), the value of distance bandwidth (BW) parameter was static, while in this study the BW was dynamically changed and determined based on the current solution of each driver every week. Here, a set of distance BW value was formed based on shift constraint. In each iteration, the BW values were often changed and randomly chosen within the set, whereas the 2-opt swapping normally used in travelling salesman problem was applied for route constraint based on some rules. These improvements are capable of reducing the repetition task that leads to fairness issue. The result demonstrated that CSAHS-2opt gave better solutions compared with standard HS, improved HS and parameter-adaptive HS.

A matheuristic for the driver scheduling problem with staff cars

In the public bus transport industry, it is estimated that the cost of a driver schedule accounts for approximately 60% of a transport company’s operational expenses. Hence, it is important for transport companies to minimize the overall cost of driver schedules. A duty is defined as the work of a driver for a day and the driver scheduling problem (DSP) is concerned with finding an optimal set of driver duties to cover a set of timetabled bus trips. Numerous labor regulations and other practical conditions enforce drivers to travel within the city network to designated bus stops to start/end duty, to take a break or to takeover a bus from another driver. This paper focuses on the driver scheduling problem with staff cars (DSPSC), where staff cars can be utilized by the drivers to fulfill their travel activities. However, staff cars should always be returned to the depot and can perform multiple round trips during the day. The problem is restricted by the number of cars available at the depot. We present a matheuristic for solving the DSPSC and the proposed method is tested on instances from Danish and Swedish companies. A comparison with a state-of-the-art mixed integer programming (MIP) solver indicates that the matheuristic provides better solutions, with comparable computation times, for 6 out of 10 large instances. For instances that have more than 6 staff cars and 1200 bus trips, the improvement is 13–15% on average.

The truck driver scheduling problem with fatigue monitoring

In the United States, approximately 4000 fatalities due to truck and bus crashes occur each year. Of these, up to 20% are estimated to involve fatigued drivers [48]. However, no model currently exists that incorporates a measure of drowsiness or fatigue into the Truck Driver Scheduling Problem (TDSP). We introduce a fatigue-aware model for determining the optimal schedule for a driver while maintaining an acceptable level of alertness as well as abiding by time windows and hours of service (HOS) regulations. Additionally, we examine a shortcoming in existing regulations, specifically related to assumptions made about the rest and alertness of a driver at the start of the workweek.

Solving a Large Real-world Bus Driver Scheduling Problem with a Multi-assignment based Heuristic Algorithm

The bus driver scheduling problem (BDSP) under study consists in finding a set of duties that covers the bus schedule from a Brazilian public transportation bus company with the objective of minimizing the total cost. A deterministic 2-phase heuristic algorithm is proposed using multiple assignment problems that arise from a model based on a weighted multipartite graph. In the first phase, the algorithm constructs an initial feasible solution by solving a number of assignment problems. In the second phase, the algorithm attempts to improve the solution by two different procedures. One procedure takes the whole set of duties and divides them in a set of partial duties which are recombined. The other procedure seeks to improve single long duties by eliminating the overtime time and inserting it into another duty. Computational tests are performed using large-scale real-world data with more than 2,300 tasks and random instances extracted from real data. Three different objective functions are analyzed. The overall results indicate that the proposed approach is competitive to solve large BDSP.

A comparison of three idling options in long-haul truck scheduling

This paper studies the Truck Driver Scheduling Problem with Idling Options (TDSP-IO), an extension of the long-haul truck driver scheduling problem with a more comprehensive objective function that accounts for driving cost, fuel cost, and idling cost. The best-known idling option is the widespread practice of keeping the vehicle engine running while the vehicle is not moving, which primarily stems from the drivers’desire to keep their vehicle at an adequate comfort level during breaks. Here, we explore two additional cleaner idling options: resting at an Electrified Parking Space (EPS) or using an Auxiliary Power Unit (APU) while idling. We also account for the initial investments associated with the equipment required for the use of these technologies. We formulate a mathematical model for the TDSP-IO under these three idling options, and we perform extensive computational experiments on realistic benchmark instances. The paper sheds light on the trade-offs between various performance indicators and offers several managerial and policy insights. Our analyses quantify the advantages of using EPSs and APUs, and show that they yield both economical and environmental benefits.

A model-based decision support system for solving vehicle routing and driver scheduling problems under hours of service regulations

In principle, hours-of-service (HOS) regulations are intended to help ensure truck drivers get adequate rest and perform safe operations. The new HOS regulations, however, may lead to substantial cost increases for regional common carriers which have already been hit hard by rising fuel prices and declining shipping demands. In addition, the new HOS regulations complicate driver schedules by not only restricting the driver's consecutive driving hours, but also expanding off-duty hours. To deal with this complex challenge, we propose a model-based decision support system (DSS) that helps determine the truck driver's working hours, rest periods, and his/her assigned truck's schedules and routes under HOS regulations. As a core of this model-based DSS, we developed a mixed-integer programming model and a simulated annealing metaheuristic for solving it. This model was also integrated with a geographical information system and relational database management system to enhance interfaces between the model and its parametric data using spatial, graphical displays.

A Column Generation Based Hyper-Heuristic to the Bus Driver Scheduling Problem

Public transit providers are facing continuous pressure to improve service quality and reduce operating costs. Bus driver scheduling is among the most studied problems in this area. Based on this, flexible and powerful optimization algorithms have thus been developed and used for many years to help them with this challenge. Particularly, real-life large and complex problem instances often need new approaches to overcome the computational difficulties in solving them. Thus, we propose a column generation based hyper-heuristic for finding near-optimal solutions. Our approach takes advantages of the benefits offered by heuristic method since the column selection mode is driven by a hyper-heuristic using various strategies for the column generation subproblem. The performance of the proposed algorithm is compared with the approaches in the literature. Computational results on real-life instances are presented and discussed.