Railroad Crew Scheduling

The objectives of crew scheduling and crew rostering in public transport can be summarized as follows: the company’s objective is to achieve a high economic performance: theoretically, this can be achieved by reducing the number of runs, practically, this can hardly be realized; therefore, the only way to save cost is on the one hand side to reduce the share of unproductive times which have to be paid and on the other hand side to shorten the time to plan or to update a crew schedule; the driver’s objective is to have a crew schedule and roster of a high quality, i. e. runs with an acceptable length of break, crew schedules with a small number or no split runs at all and rest times between subsequent runs as long as possible and so on.

Crew costs are the second-largest operating expense faced by the airline industry, after fuel. Thus, even a small improvement in the quality of a crew schedule can have significant financial impact. Decisions made earlier in the airline planning process, however, can reduce the number of options available to the crew scheduler. We address this limitation by delaying some of these earlier planning decisions--specifically, key maintenance routing decisions--and incorporating them within the crew scheduling problem. We present anextended crew pairing model that integrates crew scheduling and maintenance routing decisions. We prove theoretical results that allow us to improve the tractability of this model by decreasing the number of variables needed and by relaxing the integrality requirement of many of the remaining variables. We discuss how to solve the model both heuristically and to optimality, providing the user with the flexibility to trade off solution time and quality. We present a computational proof-of-concept to support the tractability and effectiveness of our approach.

Sue Abdinnour (“ Hawker Beechcraft Uses a New Solution Approach to Balance Assembly Lines ”) is a professor of operations management and holds the Verne and Helen Omer Professorship in Business in the W. Frank Barton School of Business at Wichita State University. Her work has been published in journals such as Decision Sciences, International Journal of Production Research, European Journal of Operational Research, and the Annals of Operations Research. Sue engages in consulting that assists companies in modeling their processes and improving their operations. She has won several research and teaching awards during her career. Marc Albers (“ Optimizing Railway Crew Scheduling at DB Schenker ”) works as a consultant for Bayer Business Services. Prior to joining Bayer he worked at the University of Cologne, where he received his doctoral degree. His fields of interest include crew scheduling, supply chain management, and business intelligence. Jude Buquid (“ HD Supply Facilities Maintenance Uses Diluted Discounts to Optimize Purchasing Opportunities ”) is the director of inventory management and logistics planning at HD Supply Facilities Maintenance. He has more than 15 years of experience across the supply chain in duties that include outbound fulfillment and freight cost optimization, applying academic theory to the realities of modern inventory management, and striking the right balance of speed and cost at which products can be delivered. He is currently focused on optimizing the company's network footprint from an inventory perspective as well as developing strategies to increase throughput through distribution centers. He holds a BS in logistics and economics from the University of Maryland at College Park and an MSBA in finance from San Diego State University. Philip Hans Franses (“ Averaging Model Forecasts and Expert Forecasts: Why Does It Work? ”) is professor of econometrics and professor of marketing research, both affiliated with the Erasmus School of Economics. His research interests concern marketing, empirical finance, applied econometrics, and forecasting. He publishes on these topics in a variety of academic journals including Interfaces, the Journal of Marketing Research, and the Journal of Econometrics. Currently he serves as the Dean of the Erasmus School of Economics, serving 5,000 students and 400 staff. Kevin C. Furman (“ Feedstock Routing in the ExxonMobil Downstream Sector ”) has been a leader of various programs and teams related to optimization and logistics research and software application development across multiple ExxonMobil affiliates. He received his PhD in chemical engineering from the University of Illinois at Urbana–Champaign. His eight years at ExxonMobil have focused on research, development, and leadership in the areas of OR and process systems engineering. David Gibson (“ HD Supply Facilities Maintenance Uses Diluted Discounts to Optimize Purchasing Opportunities ”) is the manager of logistics planning at HD Supply Facilities Maintenance and has been working within the field of operations and inventory management for the past seven years. His areas of expertise include process improvement, working capital optimization, and distribution center slotting efficiency. He is a leader in reshaping the corporate culture at HD Supply Facilities Maintenance by demonstrating innovative ways that data can be used to make decisions. He is a graduate of San Diego State University and holds a BS in financial services. Knut Haase (“ Optimizing Railway Crew Scheduling at DB Schenker ”) is a professor in the School of Business, Economics, and Social Sciences at the University of Hamburg. He received his PhD and his habilitation at the University of Kiel. His current research areas focus on crew scheduling, discrete choice models, line planning, pilgrim scheduling, and revenue management. Paul Huppert (“ HD Supply Facilities Maintenance Uses Diluted Discounts to Optimize Purchasing Opportunities ”) received his degree in business administration from San Diego State University. He is a supply chain manager for HD Supply. He has over 12 years experience in real-world inventory optimization including the implementation of supply chain systems that support the function. He is certified by the Institute of Business Forecasting as a Professional Forecaster. Silke Jütte (“ Optimizing Railway Crew Scheduling at DB Schenker ”) is a research assistant in the Department of Supply Chain Management at the University of Cologne. She has studied business mathematics at the University of Kaiserslautern and worked as a process manager at DHL. She is writing her PhD thesis in the field of crew scheduling. Gary R. Kocis (“ Feedstock Routing in the ExxonMobil Downstream Sector ”) is a senior technologist with ExxonMobil Research and Engineering Company, presently working in the supply chain optimization field. During his 10 years with ExxonMobil, he has developed and applied optimization-based solutions to refinery planning and scheduling, and logistics optimization. He has 22 years of experience as a mathematical programming practitioner, having worked in systems development for Shell Oil Company and the ROMeo online optimization tool for Invensys. Michael K. McDonald (“ Feedstock Routing in the ExxonMobil Downstream Sector ”) is an ExxonMobil Global feedstocks trader. He has been trading refining intermediates and products, and natural gas for 15 years. Jin-Hwa Song (“ Feedstock Routing in the ExxonMobil Downstream Sector ”) leads optimization research at Corporate Strategic Research, ExxonMobil Research and Engineering Company. He received his PhD from the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. Since joining ExxonMobil, he has been working on various projects related to optimization and decision science, as well as science-build research programs with several universities. Ulrich W. Thonemann (“ Optimizing Railway Crew Scheduling at DB Schenker ”) is a professor in the Department of Supply Chain Management at the University of Cologne. He received his PhD from Stanford University and worked as a management consultant at McKinsey & Company. His current research areas focus on crew scheduling, inventory optimization, and behavioral operations. Joris van de Klundert (“ ANWB Automates and Improves Service Personnel Dispatching ”) holds an MSc in computer science from Erasmus University Rotterdam and a PhD in OR from Maastricht University. He has served as the founding director of Mateum, a Maastricht University spin-off delivering OR-based software and consultancy services. After being appointed professor of value chain optimization at Maastricht University, he returned to Erasmus University Rotterdam in 2009 to chair the Department of Health Services Management and Organisation. His main research interests are in the contributions of management science to networks of health-service organizations. Peter van Huigenbosch (“ ANWB Automates and Improves Service Personnel Dispatching ”) is trained as a military officer and holds a bachelor's degree in automotive mechanics. He has worked in various positions at ANWB since 1992. He became involved in dispatch services while doing his MBA, which he earned in 2003. He is logistics manager at ANWB responsible for all supporting departments involved in assisting 1,250,000 stranded motorists annually. Philip H. Warrick (“ Feedstock Routing in the ExxonMobil Downstream Sector ”) is a Distinguished Engineering Associate with ExxonMobil Research and Engineering Company. He is responsible for the supply chain technology team. His 30-year career at ExxonMobil has concentrated on the downstream of the oil business, including responsibilities for supply, transportation and refinery operations and planning, cargo trading, and the development and application of optimization technology to refining and logistics. Laurens Wormer (“ ANWB Automates and Improves Service Personnel Dispatching ”) holds an MSc in OR from Maastricht University. He works for Mateum, a company providing advanced planning and optimization solutions for complex and innovative business processes. His main interests lie in developing decision support systems with state-of-the-art OR techniques that improve customer satisfaction and operational efficiency in health, home-care, and service organizations.

Public transport crew scheduling is a worldwide problem, which is NP-hard. This paper presents a new crew scheduling approach, called GRAVIG, which integrates grey relational analysis (GRA) into a Variable Iterated Greedy (VIG) algorithm. The GRA is served as a solver for the shift selection during the schedule construction process, which can be considered as a multiple attribute decision making (MADM) problem, since there are multiple static and dynamic criteria governing the efficiency of a shift to be selected into a schedule. Moreover, in the GRAVIG, a biased probability destruction strategy is elaborately devised to keep the ‘good’ shifts remained in the schedule without compromising the randomness. Experiments on eleven real-world crew scheduling problems show that the GRAVIG can generate high-quality solutions close to the lower bounds obtained by the CPLEX in terms of the number of shifts.

A computer based interactive approach to crew scheduling

With the network-level operation for urban rail transit systems, achieving crew resource sharing is of significant importance for resource allocation optimization, operational costs reduction, and network transport efficiency enhancement. This study introduces the multi-line crew resource sharing into crew scheduling optimization without altering the existing crew rostering patterns prevalent in urban rail transit systems. Building upon single-line scheduling approaches, the personal preferences of crew members for cross-line duty and departure/arrival location preferences are considered. An integer programming optimization model for crew scheduling is proposed to achieve collaborative optimization of network-level crew schedules. The solution algorithm employs a column-generation framework, further utilizing a column fixation strategy to enhance the quality of the solutions. A rollback method is designed to improve the column fixation process by removing columns with poor quality. A case study involving three lines in a urban rail transit network is presented to demonstrate the effectiveness of the proposed model and algorithm. The implementation of crew resource sharing is shown to reduce the total number of required crew members, while accommodating personal preferences has a minimal negative impact on the potential for scale reduction.

Crew scheduling is an important part of the passenger dedicated line plan system, and also the main factor which influences the operating expenses of passenger dedicated line. After analyzing the crew scheduling problem, the following two steps are chosen to solve this problem. Firstly, divide the train running paths into crew paths, and then combine these crew paths into crew routes according to related constrain conditions of crew scheduling plan, the relationship between train numbers and the EMU routes. A mathematical model is given with the aim of minimizing the operating expenses of the crew scheduling problem and an ant colony algorithm is designed to solve this model.

We analyze a tactical freight railway crew scheduling problem, when train drivers must be informed several weeks before operations about the start and end times and locations of their duties. Between informing the train drivers and start of operations, trip demand changes due to cancellations, new bookings, and reroutings of trains, which might result in mismatches between train driver capacity at a location and demand. We analyze an approach that incorporates uncertain trip demand as scenarios, such that the start and end times and locations of the duties of a crew schedule are recoverable robust against deviations in trip demand. We develop a column generation solution method that dynamically aggregates trips to duties and decomposes the subproblems into smaller, computationally tractable instances. Our model determines duty frames that cover duties in many scenarios, creating recoverable robust crew schedules. We test our model on three real data sets of a major European freight railway operator. Our results show that our schedules are considerably more recoverable robust than those of the nominal solution, resulting in smaller mismatches between train driver capacity and demand.

Train crew management involves the development of a duty timetable for each of the drivers (crew) to cover a given train timetable in a rail transport organization. This duty timetable is spread over a certain period, known as the roster planning horizon. Train crew management may arise either from the planning stage, when the total number of crew and crew distributions are to be determined, or from the operating stage when the number of crew at each depot is known as input data. In this paper, we are interested in train crew management in the planning stage. In the literature, train crew management is decomposed into two stages: crew scheduling and crew rostering which are solved sequentially. We propose an integrated optimization model to solve both crew scheduling and crew rostering. The model enables us to generate either cyclic rosters or non-cyclic rosters. Numerical experiments are carried out over data sets arising from a practical application.

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 airline industry has a long history of developing and applying optimization approaches to their myriad of scheduling problems. These problems have several challenging characteristics, the two most challenging of which include: 1) they span long- and short-term horizons, from strategic planning of flight schedules operated several months into the future, to real-time operations in which strategies must be developed and implemented immediately to recover scheduled operations from disruptions; and 2) they include multiple resources that must be coordinated, such as aircraft, crews, and passengers. While optimization approaches have been essential to the airline industry and effective in developing aircraft and crew schedules, historical models and approaches often fail to capture the complexity of airline operations. For example, approaches, often by necessity, involve a sequential, rather than an integrated process to develop schedules for aircraft and crews, and moreover, the process involves simplifying assumptions, including that future demands are known and deterministic, and that schedules are operated as planned. In more recent research on airline schedule optimization, advances have led to new schedule optimization models and approaches that more accurately reflect reality. As described in this presentation, the most notable contributions to these advances include: 1. Integrated Aircraft and Crew Schedule Optimization Approaches in which some of the aircraft and crew schedule decisions previously taken sequentially are integrated, moving closer to producing globally optimal schedules; 2. Dynamic Scheduling Approaches in which schedules are adjusted during the passenger booking period to reflect increased knowledge of booking patterns and to increase the schedule’s associated total revenue; and 3. Robust Optimization Approaches in which the stochastic nature of airline operations is modeled and realized schedule performance is optimized.

This paper proposes an evolutionary alternative to conventional two-phase planning methods for solving the integrated crew scheduling (ICS) problem. The approach models and formulates the ICS problem as a combinational optimization problem with multiple constraints and objectives. An integrated evolutionary framework is proposed for simultaneously considering crew pairing and crew rostering subproblems. To improve the efficiency of the Pareto set explorer, the solution methodology applies a novel variant of the nondominated sorting genetic algorithm II (NSGA-II), one of the most popular multiobjective optimization evolutionary algorithms. The proposed variant features problem-dependent constraint handling and a bounded front policy to reserve diverse individuals. The proposed approach is verified and validated in a case study of a real-world short-haul airline crew scheduling problem. The experimental results obtained by the proposed integrated approach are then compared with a real-world airline plan generated by the conventional sequential method. An aircraft schedule recovery problem is also studied to compare solution performance between the conventional NSGA-II method and the proposed NSGA-II variant. The comparison results confirm that the proposed variant obtains solutions that are superior in two aspects: First, the proposed NSGA-II variant obtains better convergence in the studied problems compared with the original version; second, the results explored by the variant enable decision makers to select from multiple crew schedules, which are superior to the real-world airline crew plan while considering the same objectives and constraints.

Nowadays, challenged by diverse uncertainties and disruptions (e.g., bad weather), as well as the strict environmental regulations imposed by authorities (e.g., on carbon emissions), airlines are struggling. How to improve their operational efficiency in such a volatile and adverse market becomes a top agenda of airlines. Among various operations, crew scheduling is fundamentally important as staffing cost is a big part of the total operational expenses. It is known that in crew scheduling, “robust crew pairing” is crucial to make the produced pairings less vulnerable in real operations. Existing studies generally construct robustness assuming that the aircraft cruise speed is fixed. However, prior studies have found that flight times exhibit significant variations due to reasons like cruise speed adjustment, and aircraft can control cruise speed for purposes like reducing delays. For crew, cruise speed controllability is also useful in hedging disruptions. For example, one flight can speed up to meet its on-time arrival even if it departs late due to crew disruptions. However, the impacts of cruise speed controllability on crew pairing robustness and the related environmental costs are under-explored. We thus propose this preliminary study to explore the possibility to use cruise speed controllability to enhance schedule robustness for crews.

The crew scheduling problem is one that has been studied almost continually for the past 40 years but all prior approaches have always approximated the problem of finding an optimal schedule for even the smallest of an airline's fleets. The problem is especially important today since costs for flying personnel of major U.S. carriers have grown and now often exceed $1.3 billion a year and are the second largest item (next to fuel cost) of the total operating cost of major U.S. carriers. Thus even small percentage savings amount to substantial dollar amounts. We present a branch-and-cut approach to solving to proven optimality large set partitioning problems arising within the airline industry. We first provide some background related to this important application and then describe the approach for solving representative problems in this problem class. The branch-and-cut solver generates cutting planes based on the underlying structure of the polytope defined by the convex hull of the feasible integer points and incorporates these cuts into a tree-search algorithm that uses automatic reformulation procedures, heuristics and linear programming technology to assist in the solution. Numerical experiments are reported for a sample of 68 large-scale real-world crew scheduling problems. These problems include both pure set partitioning problems and set partitioning problems with side constraints. These “base constraints” represent contractual labor requirements and have heretofore not been represented explicitly in the construction of crew schedules thus making it impossible to provide any measure of how far the obtained solution was from optimality. An interesting result of obtaining less costly schedules is that the crews themselves are happier with the schedules because they spend more of their duty time flying than waiting on the ground.

Optimal Multi-Vehicle Type Transit Timetabling and Vehicle Scheduling