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Driver Scheduling Problem Modelling
Abstract
The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, such as bus, train and boat drivers or plane pilots, for the transportation of passengers or goods. This is a complex problem as it involves several constraints related to labour and company rules and may also entail different evaluation criteria and objectives. The ability to develop an adequate model for this problem, which can represent the real problem as closely as possible is an important research area.
In this paper we present new mathematical models for the DSP which embody the very complexity of the drivers scheduling problem, besides demonstrating that the solutions generated by these models can easily be implemented in real situations.
On the strength of extensive passenger transportation experience in bus companies in Portugal, we propose and test new alternative models to formulate the DSP. These models are based on Set Partitioning/Covering models. Moreover, they also take into account the bus operator issues and the user’s standpoint and environment.
... Public transport services are under pressure with increased empowered user expectations. Modern transportation systems should overcome challenges of more traffic needs [1, 2], limited transportation network capacity [3, 4], design of novel transportation systems supporting sustainable cities [5][6][7][8]and increased demand for more efficient utilization of resources as operational capacities [9][10][11][12][13][14]. The speed at which the present transportation infrastructure has to accommodate growth in cities raises concerns related to over-capacity and difficult-to-use public transport. ...
... This requires that the service provider (a transport service company) is able to use specific tools for the organization of both resources (buses, bus drivers) and capacities (bus schedules). The SRR formalization is approached on the premises of the classical Bus Driver Scheduling (BDSP) problem [13]. The BDSP problem refers to a complex part of the operational planning effort in transport companies and it can be depicted on two working levels: a) setting up vehicles' routes and frequency, based on specified route lengths and transport load requirements (the B component), and b) selection of the duty set for vehicle drivers (the D component) [13,[60][61]. ...
... The SRR formalization is approached on the premises of the classical Bus Driver Scheduling (BDSP) problem [13]. The BDSP problem refers to a complex part of the operational planning effort in transport companies and it can be depicted on two working levels: a) setting up vehicles' routes and frequency, based on specified route lengths and transport load requirements (the B component), and b) selection of the duty set for vehicle drivers (the D component) [13,[60][61]. Several algorithms and tools have been used throughout referred literature to solve the above mentioned management problem in the domain of public transport services. ...
This paper shows how service science principles may be used for engineering and realizing improved public transport services. It approaches a value co-creation perspective for the management of public transport service operations based on an activity-based model of a generic service system that allows capturing requirements for software intensive service systems. The main focus is on specific implementation issues of the activity-based model of the generic service system, with a strong accent on its most representative component, the service set-up and configuring unit. This model is applied in a case study for planning of a public transport service and describes how a specific service reconfiguring request is formulated. This examination is further used as a document of requirements that drives the construction of an agent-based model expressing value-creation interactions among service system’s stakeholders in public transport services. The usefulness of the developed agent-based model for the analysis of service systems operational capabilities is suggested through simulation. A business scenario related to the management of public transport services is described, and the defined agent-based model is executed with the Presage2 multi-agent programming platform in order to capture specific issues of piece-of-work planning. The proposed approach, evaluated on the simple working scenario, fosters the role of service interaction modeling in supporting a public transport service system to dynamically adapt its operational capabilities in delivering good public transport services, as more or less quantifiable changes can affect service delivery over time.
... For crew scheduling problems, an indispensible schedule-level constraint is that each piece of vehicle work must be covered by at least one shift in the schedule. Consequently, they can be naturally represented as a set covering formulation (SCF), as usually done in previous literatures [21,24,26,30,32,34]. ...
... Other similar schedule-level constraints have also been presented to reflect some operational properties in crew scheduling. The reader can be referred to Ernst et al. [12], Dias et al. [11], Portugal et al. [32] and Abbink at al. [3]. Another reason is that the standard SCF cannot reflect the transit operators' preferences or expectations about some special types of shifts. ...
... Although the preferences can be handled by imposing a big penalty cost to the non-preferred shifts [2], it will spend much time to adjust the penalty costs such that the solutions fit for the operator's expectation. Moreover, setting the values of penalty costs often frustrates the human schedulers lacking optimization knowledge [32]. In many cases, transit operators' requirements are hard constraints that must be satisfied. ...
Crew scheduling in public transport is to cut vehicle works to a set of feasible shifts which are implemented by crews or drivers. Most crew scheduling problems are often based on standard set covering formulations, which cannot meet some particular requirements imposed on shift generation, for example, the number or the percentage of a particular type of shifts must be within a predefined range. Taking the realistic characteristics of crew scheduling into account, an extended set covering formulation with three types of additional constraints is proposed to satisfy various specific requirements and constraints. A column generation algorithm is presented to solve the formulation. To deal with the difficulties brought by additional constraints, a decomposition strategy is proposed to solve the column generation subproblems, in which all shifts are reclassified into several sets of disjoint shifts according to the types of additional constraints, and each subproblem corresponds to the generation of one set of shifts in a directed graph. Moreover, a branching strategy based on relief opportunities is designed to get integer solutions. The proposed model and algorithms are tested on twelve instances derived from real-world problems. The experimental results show that the schedules satisfying to the transit operators' requirements are produced.
... Since the DSP is a practical problem, models have been developed in collaboration with planners and end-users of transport companies so that complexities that arise in practice are considered. Some examples include Smith and Wren (1988), Wren et al. (2003) and Portugal et al. (2009), where the authors heuristically generate a feasible subset of variables that comply with the labor regulations and the transport companies' rules. The largest instance considered by Smith and Wren (1988) involved 309 bus trips and 4,892 variables in the SCP formulation. ...
... The largest instance considered by Smith and Wren (1988) involved 309 bus trips and 4,892 variables in the SCP formulation. Portugal et al. (2009) tested the models on instances from several transport companies in Portugal that had up to 347 bus trips and 23,305 variables. Some authors have considered solving the SCP formulation by metaheuristic procedures. ...
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%.
... The Driver Scheduling Problem (DSP) is another large area of research in the personnel scheduling. DSP consists of selecting a set of duties for the drivers or pilots of vehicles, (e.g., buses, trains, boats, or planes) for the transportation of passengers or goods (Portugal et al., 2009). The DSP can also be divided into sub-categories such as Bus Driver Scheduling Problem (BDSP), Truck Driver Scheduling Problem (TDSP). ...
In this paper, we consider a problem inspired by a real-life problem, which aims to schedule high multiplicity jobs on a single machine by taking into account the organization-specific constraints in a different schedule structure. The schedule is daily with daytime and nighttime periods. The operator is considered as an additional resource that varies in terms of consumption and scheduling depending on the period. There are specific rest periods before and after night-period jobs, and night-period jobs affect both the daily working time and number of the jobs in the daytime- period. In addition, the operator's daily workload is divided into two categories: normal and heavy. If the workload is heavy on consecutive days, specific rest periods must be scheduled. The integer programming model of the problem is presented. The feasible solutions obtained in a short time with greedy constructive heuristic algorithms are used in the exact solution approach as both upper bound and warm-start point. Finally, the effectiveness of the solution approaches is compared and evaluated through numerical experiments carried out for a variety of problem instances of different sizes.
... The driver scheduling problem consists in selecting a set of duties for vehicle drivers. It is a well-known problem, and various models, possible objective functions and constraints can be found in (Portugal and co HRL, Paixão JP, 2009;Wren et al. 2003), whereas some case studies are presented in Kwan (2011). The most common contract-related constraints for drivers, which are also present in our problem, are the following: maximum duty length, minimum break duration, maximum time without break, and multiple driver depots (Abbink et al. 2005;Boschetti et al. 2004;Fores et al. 2002;Yunes et al. 2005). ...
At the scale of Switzerland, the national railway company SBB Cargo AG has to schedule its locomotives and drivers in order to be able to pull all trains. Two objective functions are considered in a two-stage lexicographic fashion: (1) the locomotive and driver costs and (2) the driver time that is spent without driving. As the problem instances tend to reach really big sizes (up to 1900 trains), we propose to schedule locomotives and drivers in a sequential way, thus having a sequence of smaller problems to solve. Moreover, for smaller instances, we also propose to schedule jointly locomotives and drivers in an integrated way, therefore increasing the search space but possibly leading to better solutions. In this paper, we present a mathematical formulation and model for the problem. We also consider the contract-related constraints of the drivers, and we propose a way to integrate some time flexibility in the schedules. Next, we propose an innovative matheuristic to solve the problem, relying on a descent local search and a rolling horizon decomposition. An important goal of this method is to explore thoroughly at which extent a general-purpose solver can be used on this problem. Finally, the benefits of each aspect of the model and of the method are analyzed in detail on the results obtained for 20 real SBB Cargo AG instances.
... Research on bus driver scheduling problems has a long history (Wren and Rousseau 1995) and uses a variety of solution methods. Exact methods mostly use column generation with a set covering or set partitioning master problem and a resource constrained shortest path subproblem (Smith and Wren 1988;Desrochers and Soumis 1989;Portugal, Lourenço, and Paixão 2009;Lin and Hsu 2016). Heuristic methods like greedy (Martello and Toth 1986;De Leone, Festa, and Marchitto 2011;Tóth and Krész 2013) or exhaustive (Chen et al. 2013) search, tabu search (Lourenço, Paixão, and Portugal 2001;Shen and Kwan 2001), genetic algorithms (Lourenço, Paixão, and Portugal 2001;Li and Kwan 2003), or iterated assignment problems (Constantino et al. 2017) are used in different variations. ...
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.
... Different variants of BDSPs have been studied from the early 60's [17]. Regarding exact methods, the BDSP is often modelled as a Set Partitioning Problem and column generation is often used [6,8,13,15]. However, due to the need to solve very large real-world problems in a reasonable time, several heuristic methods have been studied for BDSP: some examples are Greedy [12], Tabu Search [14], Simulated Annealing [5], GRASP [2], and Genetic Algorithm [7,11]. ...
The Bus Driver Scheduling Problem (BDSP) is a combinatorial op-timisation problem that consists of assigning bus drivers to vehicles with predetermined routes. The objective is to optimise the em-ployees' operating costs and work quality based on goals like the number of vehicle changes. This problem is highly constrained due to the complex rules specified by a collective agreement and law. Hence, solving real-life instances with exact methods in a reasonable time is very challenging. In this work, we investigate and compare metaheuristics based on Tabu Search and Iterated Local Search for solving this problem. We analyse the impact of different solution components, including neighbourhoods, acceptance criteria, tabu lists, and perturbation moves. Further, we provide a new set of large real-life-based instances that extends the existing benchmark. We compare our methods with the state-of-the-art approaches on the extended set of instances and show that our algorithms provide very good solutions for large instances.
... En otras palabras, DSP se encarga de calendarizar las actividades que deben realizar los conductores sin personalizar. Portugal et al. (2009) mencionan que los deberes o actividades hacen referencia a: ...
Existe en la actualidad un crecimiento acelerado de las ciudades, debido principalmente a la migración de las personas buscando mejorar su calidad de vida. Esto ha provocado el surgimiento de diversas problemáticas, como por ejemplo: abastecimiento de agua y energía eléctrica, problemas de salud, alimentación, educación y contaminación, entre otros. Uno de los problemas más importantes y del cual se derivan en mayor o menor medida algunos de los antes mencionados, es el del transporte público. Desde hace varias décadas algunos investigadores han abordado esta problemática desde diferentes perspectivas y aplicando diferentes técnicas para solucionarlos y generalmente poniéndole un acrónimo particular. El presente trabajo muestra una revisión de los principales tipos de problemas de redes de transporte público abordados a lo largo de estos últimos años y busca clasificar los tipos de problemáticas abordadas. Como se puede ver, varios de los problemas planteados con diferentes nombre corresponden al mismo tipo de problema. En general, este tipo de problemas sigue teniendo un gran interés en la actualidad debido a la importancia que representa la solución de éstos.
... The objective was to find a way to maximize driver employment and optimize some of the economic objectives of the company in real-time and company resources management (e.g., scheduled drives could be canceled or modified at the last minute according to customer requirements). The main objective of the research done by Portugal, Lourenço, Paixão (2009) was to introduce new mathematical models explaining the complexity of crew planning and to present the easiness of the implementation of these models into real situations. The researchers introduced a generalized crew planning problem, where the user requirements are considered. ...
It is indisputable that the continuous development of digital technologies influences the business environment. Using information technologies means easier access to a huge amount of business information, which is hard to include in day-to-day decision-making. Traditional data processing methods in business management become inadequate. So, business process management approaches and business data analysis are the tools that could be utilized to optimize processes in a company and to harvest valuable information that can provide a variety of decision-making material for company management. This article deals with the analysis, modeling, and optimization of the transport process, as well as the design of a system for decision support in this process within a small transport company. The research is focused on the development of an innovative decision support system based on a company’s data analysis in order to improve the management of the transport service process.
... The authors focused more on combining theory and practice to create a user-friendly and flexible system. Portugal, Lourenço & Paixão (2009) presented SCP based models that were developed in collaboration with planners and end-users of several transport companies in Portugal. The authors aimed at developing models to produce solutions that could be applied in real situations and, hence solution quality was not the only criteria for evaluating models. ...
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.
... Another group of problems is the Vehicle Scheduling Problem (VSP), which is related to the problem of route determination for vehicles (VRP), which in many cases are considered simultaneously. A different group are the problems Crew Sheduling Problem (CSP) or Driver Sheduling Problem (DPS) regarding the issues of scheduling drivers' work at fixed transport tasks [20], [21], [22], [23]. ...
Deliveries of goods in urban agglomeration distribution systems are conditioned by many factors resulting from the specificity and character of these agglomerations. Urban agglomerations, as a specific spatial and structural system or a multi-layered spatial structure, with a specific location, spatial organization and functioning, require a systematic approach to the design of distribution systems. The article presents the characteristics of urban agglomerations and their specificity from the point of transport issues as an element of the distribution system. In addition, these factors were identified that affect the organization of deliveries and determine boundary conditions. A mathematical approach to the problem of deliveries in urban agglomeration distribution systems for the assumed decision situation was also presented. Theoretical considerations have been implemented in the case study of the urban agglomeration distribution system.
... To solve this problem, the Depth First Search Algorithm with Trip Calculation Method was suggested. (Portugal et al. 2009) treated a general driver scheduling problem striving to present new mathematical models for this problem. This latter was solved by the production of a Set Partitioning/ Covering Model. ...
In this paper, we suggest to present a literature review of the truck drivers scheduling problem since the year 2000 and to classify them to four criteria in which the main objective is to offer a complete reference frame grouping the works dedicated to the truck driver scheduling. The literature review presents a brief summary of every article specifying the context, the methodology of research and the results and proposes research leads relative to the type of problems.
... By implementing Lagrangian Relaxation (LR) and CG, the authors are able to handle the constraints and generate bounding procedures, leading to a more efficient implementation of the proposed CG approach. Although there are several formulations in the literature, Portugal et al. (2009) states that the classical set partition/set covering model simplifies some of the specific business aspects and issues of real problems, making it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually in order to be implemented in real situations. Then, the authors use the actual observations of a transport network agency in Portugal to develop several mathematical formulations with evaluation criteria such as total ''real'' cost, not covered work by number of pieces, and not covered work duration of pieces. ...
The efficiency of a transport system depends on several elements, such as available technology, governmental policies, the planning process, and control strategies. Indeed, the interaction between these elements is quite complex, leading to intractable decision making problems. The planning process and real-time control strategies have been widely studied in recent years, and there are several practical implementations with promising results. In this paper, we review the literature on Transit Network Planning problems and real-time control strategies suitable to bus transport systems. Our goal is to present a comprehensive review, emphasizing recent studies as well as works not addressed in previous reviews.
... V. SCHEDULING PARAMETERS:-There are different scheduling problems present in project scheduling such as Bus driver scheduling problem, employee scheduling problem, etc having set of parameters. According to Helena Ramalhinho Lourenço, bus driver scheduling problem finding the minimum cost and set of feasible daily duties that cover all the trips to meet heuristic approach [5]. General employee scheduling problem arises in variety of service delivery settings, including scheduling of nurses in hospital ,check encoders in bank, hotel, hospital ,petrol offices etc [17]. ...
In project management ,mainly scheduling refers to a
set of policies and mechanisms to control the order of work
performed .In scheduling of project there are many problems such
as general employee scheduling problem, Bus driver scheduling
problem, Scheduling problem in self suspending tasks. Resource
scheduling problem ,university class scheduling problem and so
on.
Conflict measurement is one of the key tasks for project
scheduling. This work is mainly focusing on parameters that
affects to conflicts in project scheduling &identification of
conflicts .This work gives the related work that create conflict
free schedule while maintaining the resource constraints done by
various authors.
... The road passenger transportation problem fits neatly into the category of optimization problems, in which resources (drivers) have to be assigned to tasks (transport services) fulfilling some constraints and minimizing some function cost. Although in most cases these problems are solved by state-of-the-art techniques, there are still a lot of recent papers dealing with the driver allocation problem, such as Abbink et al. (2007), Portugal et al. (2006), and Laplagne et al. (2005, indicating that the problem is still open, due to the different problem specificities the engineers have to tackle. There do not appear to be any general guidelines for choosing the appropriate technique given the specific description of a problem. ...
Analyzing the state of the art in a given field in order to tackle a new problem is always a mandatory task. Literature provides surveys based on summaries of previous studies, which are often based on theoretical descriptions of the methods. An engineer, however, requires some evidence from experimental evaluations in order to make the appropriate decision when selecting a technique for a problem. This is what we have done in this paper: experimentally analyzed a set of representative state-of-the-art techniques in the problem we are dealing with, namely, the road passenger transportation problem. This is an optimization problem in which drivers should be assigned to transport services, fulfilling some constraints and minimizing some function cost. The experimental results have provided us with good knowledge of the properties of several methods, such as modeling expressiveness, anytime behavior, computational time, memory requirements, parameters, and free downloadable tools. Based on our experience, we are able to choose a technique to solve our problem. We hope that this analysis is also helpful for other engineers facing a similar problem.
... In contrast, the proposed MSR problem is to find a subset locations of given N locations for recommendation. Also, the MSR problem is different from the traditional scheduling problem [8,17], which selects a set of duties for vehicle drivers. The reason is that all these duties are determined in advance, such as delivering the packages to determined loca-tions, while the MSR problem consists of uncertain pick-up jobs among several locations. ...
The increasing availability of large-scale location traces creates unprecedent opportunities to change the paradigm for knowledge discovery in transportation systems. A particularly promising area is to extract energy-efficient transportation patterns (green knowledge), which can be used as guidance for reducing inefficiencies in energy consumption of transportation sectors. However, extracting green knowledge from location traces is not a trivial task. Conventional data analysis tools are usually not customized for handling the massive quantity, complex, dynamic, and distributed nature of location traces. To that end, in this paper, we provide a focused study of extracting energy-efficient transportation patterns from location traces. Specifically, we have the initial focus on a sequence of mobile recommendations. As a case study, we develop a mobile recommender system which has the ability in recommending a sequence of pick-up points for taxi drivers or a sequence of potential parking positions. The goal of this mobile recommendation system is to maximize the probability of business success. Along this line, we provide a Potential Travel Distance (PTD) function for evaluating each candidate sequence. This PTD function possesses a monotone property which can be used to effectively prune the search space. Based on this PTD function, we develop two algorithms, LCP and SkyRoute, for finding the recommended routes. Finally, experimental results show that the proposed system can provide effective mobile sequential recommendation and the knowledge extracted from location traces can be used for coaching drivers and leading to the efficient use of energy.
The railway crew scheduling problem consists of finding the most efficient duty combination for railway crews to cover all trains and related activities for a defined period of time. Crew scheduling problems in transportation originate in airline and bus industries. In the 1990s, researchers developed sophisticated algorithms which were capable of solving the larger and more complex problem instances of railway operators. Practical implementations and decision support tools received very satisfying feedback from the industry. Since then, numerous real-world problems have been studied requiring innovative algorithmic approaches to the NP-hard problem. In this paper, we review 123 articles on railway crew scheduling focusing on more recent publications since 2000. After depicting crew scheduling in railway including the differences between transportation modes, our goal is to classify the literature according to model formulations, objectives, constraints and solution methods. By systematizing the collected articles, we identify research opportunities including integrated approaches with other planning stages, real-time re- scheduling and a further investigation of the impact of robustness and employee satisfaction on the cost of railway crew schedules.
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.
In this paper we study a specific variant of the well known Fixed Job Scheduling Problem, namely the Tactical Fixed Job Scheduling Problem with Spread-Time constraints. In this problem it is required to schedule a number of jobs on non identical machines that differ each other for the set of jobs they can perform and that have constraints on the length of their duty. We present some lower bounds for the optimal value of the problem and introduce the first heuristic algorithm for solving it. We also study a specific case of interest connected with the assistance of passengers with special needs in large scale airports.
This paper suggests O(m) polynomial time heuristic algorithm to obtain the solution for the driver scheduling problem, DSP, that has been classified as NP-complete problem. The proposed algorithm gets the initial assignment of n minimum number of drivers from given m schedules. Nextly, this algorithm gets the minimum total time (TC) using 5 rules of swap and insert for decrease of over times (OT) and idle times (IT). Although this algorithm is a heuristic polynomial time algorithm with O(m) time complexity rules to be find a optimal (or approximate) solution, this algorithm is equal to metaheuristic methods for the 5 experimental data. To conclude, this paper shows the DSP is not NP-complete problem but Polynomial time (P)-problem with polynomial time rules.
The Labour Scheduling problem in the context of any transport company is a complex optimization problem of that belongs to the class of NP-Hard problems. In these cases, it is not viable to try to find an exact solution and therefore, they require methods that assure the optimal management of the available resources in the tracing of the work calendars under the most suitable criteria of economy of times and costs. The main purpose of this research is to propose an efficient method to determine optimal shifts in a generic transport company, using bio-inspired methods. This method employs a two-step approach to obtain a solution. In a first stage, a Grasp algorithm is used to generate a viable solution. Then in a second stage, this preliminary solution is tuned, in order to obtain an optimal one, by using a Scatter Search algorithm.
The bus crew scheduling problem (BCSP) is to assign drivers and conductors to daily crew duties that cover a set of schedules for buses of a public bus company during a period of time, e.g., a week. By combining case-based reasoning (CBR) and rule-based reasoning (RBR), this paper introduces the design and implementation of a bus crew scheduling system (BCSS). The current system works like this. Firstly, an inference mechanism integrating CBR and RBR is designed to obtain near-optimal solutions. Secondly, based on these near-optimal solutions, a genetic algorithm is developed to produce better solutions. The practical applications show that the system is effective.
This paper examines time windows for scheduled trips in multiple depot vehicle and crew scheduling problems that arise in public bus transportation. In practice, the two planning tasks vehicle scheduling and crew scheduling are traditionally solved sequentially with the implicit understanding that the scheduled time for timetabled trips remains fixed. In order to improve cost efficiency two concepts have been developed over the last years: In order to obtain better flexibility when scheduling crews, vehicle and crew scheduling problems are tackled simultaneously. In order to extend flexibility while scheduling vehicles, variable trip departure and arrival times are considered. Obviously the combination of both concepts promises the largest savings, but probably leads to bursting computational times due to growing problem complexity.
In this paper we combine both concepts by extending the integrated vehicle and crew scheduling problem with the possibility to shift scheduled trips within defined time windows. We examine the tradeoffs between solution quality and computational time for different solution approaches.
The problem of mobile sequential recommendation is presented to suggest a
route connecting some pick-up points for a taxi driver so that he/she is more
likely to get passengers with less travel cost. Essentially, a key challenge of
this problem is its high computational complexity. In this paper, we propose a
dynamical programming based method to solve this problem. Our method consists
of two separate stages: an offline pre-processing stage and an online search
stage. The offline stage pre-computes optimal potential sequence candidates
from a set of pick-up points, and the online stage selects the optimal driving
route based on the pre-computed sequences with the current position of an empty
taxi. Specifically, for the offline pre-computation, a backward incremental
sequence generation algorithm is proposed based on the iterative property of
the cost function. Simultaneously, an incremental pruning policy is adopted in
the process of sequence generation to reduce the search space of the potential
sequences effectively. In addition, a batch pruning algorithm can also be
applied to the generated potential sequences to remove the non-optimal ones of
a certain length. Since the pruning effect continuously increases with the
increase of the sequence length, our method can search the optimal driving
route efficiently in the remaining potential sequence candidates. Experimental
results on real and synthetic data sets show that the pruning percentage of our
method is significantly improved compared to the state-of-the-art methods,
which makes our method can be used to handle the problem of mobile sequential
recommendation with more pick-up points and to search the optimal driving
routes in arbitrary length ranges.
We proposed several hybridizations of Reactive GRASP (Greedy Randomized Adaptive Search Procedure) with Path-Relinking (PR) and Variable Neighborhood Search to determine high-quality solutions for a Bus Driver Scheduling Problem (BDSP) under special constraints imposed by Italian transportation rules and mathematical statement originated by our collaboration with PluService Srl, leading Italian group in software for transportation companies. Experimental results are reported for all different proposed techniques that have been tested both on Italian real-world instances and random instances described and used by Huisman et al. (2005).
The Bus Driver Rostering Problem (BRP) refers to the assignment of drivers to the daily crew duties that cover a set of schedules
for buses of a company during a planning period of a given duration, e.g., a month. An assignment such as this, denoted as
roster, must comply with legal and institutional rules, namely Labour Law, labour agreements and the company’s regulations.
This paper presents a new bi-objective model for the BRP, assuming a non-cyclic rostering context. One such model is appropriate
to deal with the specific and diverse requirements of individual drivers, e.g. absences. Two evolutionary heuristics, differing
as to the strategies adopted to approach the Pareto frontier, are described for the BRP. The first one, following a utopian
strategy, extends elitism to include an infeasible (utopic) and two potential lexicographic individuals in the population,
and the second one is an adapted version of the well known SPEA2 (Strength Pareto Evolutionary Algorithm). The heuristics’
empirical performance was studied through computational tests on BRP instances generated from the solution of integrated vehicle-crew
scheduling problems, along with the rules of a public transit company operating in Portugal. This research shows that both
methodologies are adequate to tackle these instances. However, the second one is, in general, the more favourable. In reasonable
computation times they provide the company’s planning department with several rosters that satisfy all the constraints, an
achievement which is very difficult to obtain manually. In addition, among these rosters they identify the potentially efficient
ones with respect to the BRP model’s two objectives, one concerning the interests of administration, the other the interests
of the workers. Both heuristics have advantages and drawbacks. This suggests that they should be used complementarily. On
the other hand, the heuristics can, with little effort, be adapted to a wide variety of rostering rules.
Driver scheduling is an important part of the base of blocking. A better method of driver scheduling is advanced in this paper. First, a model is built, the optimization objective of which includes the opportunity cost of shifts and the least wage cost. Then a genetic algorithm is designed to get the optimization solution, and the driver scheduling model and algorithm is tested by the data of Route 115, Shijiazhuang, China. The result of the example indicates that the optimization scheme generated by the proposed method is better than original manual programming, and the solution process is simple and fast, which shows the validity of the approach.
This paper addresses the problem of determining the best scheduling for Bus Drivers, a -hard problem consisting of finding the minimum number of drivers to cover a set of Pieces-Of-Work (POWs) subject to a variety
of rules and regulations that must be enforced such as spreadover and working time. This problem is known in literature as
Crew Scheduling Problem and, in particular in public transportation, it is designated as Bus Driver Scheduling Problem. We
propose a new mathematical formulation of a Bus Driver Scheduling Problem under special constraints imposed by Italian transportation
rules. Unfortunately, this model can only be usefully applied to small or medium size problem instances. For large instances,
a Greedy Randomized Adaptive Search Procedure (GRASP) is proposed. Results are reported for a set of real-word problems and
comparison is made with an exact method. Moreover, we report a comparison of the computational results obtained with our GRASP
procedure with the results obtained by Huisman et al. (Transp. Sci. 39(4):491–502, 2005).
Driver fatigue is the cause of many truck crashes taking place today. In order to improve safety, the Federal Motor Carrier Safety Administration (FMCSA) has implemented revised Hours-of-Service (HOS) regulations effective on October 1^st 2005. According to the revised rules, drivers should take a break of 10 consecutive hours after 11 hours of driving time or 14 hours of duty time that includes driving time and service time such as loading and unloading cargo. This has caused a severe increase in the cost for the trucking industry which in turn hurt shippers and ultimately customers. A systematic way for routing vehicles to avoid traffic congestion and waiting due to truck arrival outside the customer service windows, as well as coordinating the timing drivers are taking their mandatory breaks, can improve the efficiency and safety of supply chain distribution operations. In this Thesis, a single truck routing and driver scheduling model with time-dependent travel times, HOS regulations, multiple delivery locations and service time windows is formulated and solved. The objective is to minimize the total time required to serve a given number of customers. The components of the total time are travel time, driver's break time, and waiting time and service time at the customer locations. For each segment of the transportation network, traffic congestion is modeled by using speed distribution profiles over the course of a day, which in turn makes the time required to traverse a highway segment dependent on the time the truck started traversing it. For a given set of customer locations, the optimization model determines the order in which they should be visited and the route between the consecutive customer locations in order to minimize the time of the tour subject to service time windows, HOS restrictions and time-dependent highway traversal times. A Simulated Annealing metaheuristic is implemented to obtain near optimal solutions of the problem. Our experimental results show that the heuristic provides good quality solutions for large size problems (with an average deviation of less than 1% from the optimal) in reasonable computation time. The accuracy comparison was obtained by solving smaller size problems consisting ofAnnouncement of 10 customers by explicit enumeration. The mathematical model and the solution approach can be easily adapted to more complex problems involving multiple capacitated vehicles with pickup and delivery.
In this paper we present a genetic algorithm-based heuristic for solving the set partitioning problem. The set partitioning problem is an important combinatorial optimisation problem used by many airlines as a mathematical model for flight crew scheduling. We develop a steady-state genetic algorithm in conjunction with a specialised heuristic feasibility operator for solving the set partitioning problem. Some basic genetic algorithm components, such as fitness definition, parent selection and population replacement are modified. The performance of our algorithm is evaluated on a large set of real-world set partitioning problems provided by the airline industry. Computational results show that the genetic algorithm-based heuristic is capable of producing highquality solutions. In addition a number of the ideas presented (separate fitness, unfitness scores and subgroup population replacement) are applicable to any genetic algorithm for constrained problems. Keywords: combinator...
A genetic algorithm for the set partitioning problem. Imperial College Introduction to operations research. McGraw-Hill A new approach for the drivers scheduling problem in transportation companies Operations research: principles and practice Operations research: applications and algorithms
- P Beasley
- F Hillier
- Lieberman
P, Beasley J (1995) A genetic algorithm for the set partitioning problem. Imperial College, London Hillier F, Lieberman G (1995) Introduction to operations research. McGraw-Hill, New York Portugal R (2006) A new approach for the drivers scheduling problem in transportation companies. PhD thesis, Department of Statistics and Operations Research, University of Lisbon, Portugal Ravindran A, Phillips D, Solberg J (1987) Operations research: principles and practice. Wiley, New York Winston W (1994) Operations research: applications and algorithms, 3rd edn. Duxbury Press, Pacific Grove
Master thesis Public transportation to the fORe! Or
- Agra
Agra A (1993) Master thesis, Department of Statistics and Operations Research, University of Lisbon, Portugal Borndörfer R, Grötschel M, Pfetsch E (2006) Public transportation to the fORe! Or/MS Today 33(2):30– 40
A new approach for the drivers scheduling problem in transportation companies
- R Portugal
Master thesis, Department of Statistics and Operations Research Public transportation to the fORe! Or
- A Agra
- R Borndörfer
- M Grötschel
- E Pfetsch
Agra A (1993) Master thesis, Department of Statistics and Operations Research, University of Lisbon,
Portugal
Borndörfer R, Grötschel M, Pfetsch E (2006) Public transportation to the fORe! Or/MS Today 33(2):3040
A genetic algorithm for the set partitioning problem Introduction to operations research A new approach for the drivers scheduling problem in transportation companies Operations research: principles and practice Operations research: applications and algorithms
- P Chu
- J Beasley
- F Hillier
- G Lieberman
- D Phillips
- J Solberg
Chu P, Beasley J (1995) A genetic algorithm for the set partitioning problem. Imperial College, London
Hillier F, Lieberman G (1995) Introduction to operations research. McGraw-Hill, New York
Portugal R (2006) A new approach for the drivers scheduling problem in transportation companies. PhD
thesis, Department of Statistics and Operations Research, University of Lisbon, Portugal
Ravindran A, Phillips D, Solberg J (1987) Operations research: principles and practice. Wiley, New York
Winston W (1994) Operations research: applications and algorithms, 3rd edn. Duxbury Press, Pacific
Grove