A variable iterated greedy algorithm based on grey relational analysis for crew scheduling

The salinity of the soil affects crop productivity. Approximately 20% of the total cropland and 33% of irrigated agricultural areas are salinized worldwide. Therefore, saline barren areas require plants that are tolerant of high saline levels. The objective of the current study is to investigate Eucalyptus clones that can thrive in high saline conditions. To achieve this goal, fifty Eucalyptus clones (E. camaldulensis, E. tereticornis) were irrigated with saline water (120 mM NaCl and 50 mM Na2SO4, electrical conductivity ≥20 dS ) for 3 months. To screen salt-tolerant clones, physiological, biochemical, and growth responses of clones were measured. The best performing clones under salt stress were chosen using Grey Relational Analysis (GRA), a Multiple Attribute Decision-Making (MADM) model, which is a novel approach to deal with this kind of screening study. As a result, the rank of (tolerant, moderate, and susceptible) clones was calculated, based on Grey Relational Grade (GRG). The value of GRG was based on the physio-morphological and biochemical responses of clones, indicating their greater ability to withstand saline stress. Results of this study suggest some salt-tolerant clones for the utilization of salt-affected locations to grow Eucalyptus plants, which may help to increase forest sustainability.

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.

Many decision making problems of business and management are formulated in terms of Multiple Attribute Decision Making (MADM): given a set of alternatives evaluated with multiple criteria, find the alternative which according to the Decision Maker (DM), has the most preferred combination of criteria values (attributes), or rank alternatives from the most preferred one to the least preferred one. The MADM methods incorporate mechanisms of building preference models based on information obtained from the DM. In a wide variety of such methods, the DM is supposed to provide information in terms of weights of criteria, usually understood as criteria’s priorities. These weights serve as parameters of the method-pecific preference models. The DM can define weights directly, or by using special weight elicitation techniques such as AHP, MAVT and others. Our concerns are that when using weight-based methods, the DM cannot ensure the correctness of the preference model. First, different weight-based methods use different kinds of preference models, which prioritize criteria based on weights in different manners. Second, interpretation of weights in some MADM methods is far from intuitive. Thus, a situation may occur when an inexperienced DM thinks of weights differently than they actually work in the method, and expresses the preference information incorrectly. In this paper we demonstrate the differences between how weights are interpreted in several methods: simple additive weighting, TOPSIS, VIKOR and PROMETHEE. We do it by comparing rankings produced with methods based on randomly generated data. We demonstrate that differences of interpreting weights significantly contribute to differences in produced rankings. A solution to this problem could be twofold: first, increasing awareness of differences between method-specific weight-based prioritizing mechanisms, and second, providing interpretations of weights for popular methods in the language understandable by the DMs.

A computer based interactive approach to crew scheduling

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.

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.

We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows and 1,000,000 columns, arising from crew scheduling in the Italian Railway Company, Ferrovie dello Stato SpA. In 1994 Ferrovie dello Stato SpA, jointly with the Italian Operational Research Society, organized a competition, called FASTER, intended to promote the development of algorithms capable of producing good solutions for these instances, since the classical approaches meet with considerable difficulties in tackling them. The main characteristics of the algorithm we propose are (1) a dynamic pricing scheme for the variables, akin to that used for solving large-scale LPs, to be coupled with subgradient optimization and greedy algorithms, and (2) the systematic use of column fixing to obtain improved solutions. Moreover, we propose a number of improvements on the standard way of defining the step-size and the ascent direction within the subgradient optimization procedure, and the scores within the greedy algorithms. Finally, an effective refining procedure is proposed. Our code won the first prize in the FASTER competition, giving the best solution value for all the proposed instances. The algorithm was also tested on the test instances from the literature: in 92 out of the 94 instances in our test bed we found, within short computing time, the optimal (or the best known) solution. Moreover, among the 18 instances for which the optimum is not known, in 6 cases our solution is better than any other solution found by previous techniques.

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.

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.

The set covering problem has many diverse applications to problems arising in crew scheduling, facility location and other business areas. Since the problem is known to be hard to solve optimally, a number of approximate (heuristic) approaches have been designed for it. These approaches (with one exception) divide into two main groups, greedy heuristics and dual saturation heuristics. We use the concept of a Pareto optimal dual solution to show that an arbitrary dual saturation heuristic has the same worst-case performance guarantee as the two best known heuristics of that type. Moreover, this poor performance level is always attainable by those two heuristics.

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.

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.

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.

PurposeThe purpose of this paper is to optimise the process parameters, namely, fibre orientation angle, helix angle, spindle speed, and feed rate in milling of glass fibre-reinforced plastic (GFRP) composites using grey relational analysis (GRA) and desirability function analysis (DFA).Design/methodology/approachIn this work, experiments were carried out as per the Taguchi experimental design and an L27 orthogonal array was used to study the influence of various combinations of process parameters on surface roughness and delamination factor. As a dynamic approach, the multiple response optimisation was carried out using GRA and DFA for simultaneous evaluation. These two methods are best suited for multiple criteria evaluation and are also not much complicated.FindingsThe process parameters were found optimum at a fibre orientation angle of 15°, helix angle of 25°, spindle speed of 6,000 rpm, and a feed rate of 0.04 mm/rev. Analysis of variance was employed to classify the significant parameters affecting the responses. The results indicate that the fibre orientation angle is the most significant parameter preceded by helix angle, feed rate, and spindle speed for GFRP composites.Originality/valueAn attempt to optimise surface roughness and delamination factor together by combined approach of GRA and DFA has not been previously done.

Railway crew scheduling deals with generating driver duties for a given train timetable such that all work regulations are met and the resulting schedule has minimal cost. Typical problem instances in the freight railway industry require the generation of duties for thousands of drivers operating tens of thousands of trains per week. Due to short runtime requirements, common solution approaches decompose the optimization problem into smaller subproblems that are solved separately. Several studies have shown that the way of decomposing the problem significantly affects the solution quality. An overall best decomposition strategy for a freight railway crew scheduling problem, though, is not known. In this paper, we present general considerations on when to assign two scheduled train movements to separate subproblems (and when to rather assign them to the same subproblem) and deduct a graph partitioning based decomposition algorithm with several variations. Using a set of real-world problem instances from a major European railway freight carrier, we evaluate our strategy and benchmark the performance of the decomposition algorithm both against a common non-decomposition algorithm and a lower bound on the optimal solution schedule. The test runs show that our decomposition algorithm is capable of producing high-quality solution schedules while significantly cutting runtimes compared to the non-decomposition solution algorithm. We are following a "greenfield" approach, where no information on previous schedules is needed. Hence, our approach is applicable to any railway crew scheduling setting, including network enlargement, integration of new customers, etc.