Timetable Optimization Research Articles

Domain transformation approach to deterministic optimization of examination timetables

In this paper we introduce a new optimization method for the examinations scheduling problem. Rather than attempting direct optimization of assignments of exams to specific time-slots, we perform permutations of slots and reassignments of exams upon the feasible (but not optimal) schedules obtained by the standard graph colouring method with Largest Degree ordering. The proposed optimization methods have been evaluated on the University of Toronto, University of Nottingham and International Timetabling Competition (ITC2007) datasets. It is shown that the proposed method delivers competitive results compared to other constructive methods in the timetabling literature on both the Nottingham and Toronto datasets, and it maintains the same optimization pattern of the solution improvement on the ITC2007 dataset. A deterministic pattern obtained for all benchmark datasets, makes the proposed method more understandable to the users.

Integrating optimization and data mining techniques for high-speed train timetable design considering disturbances

Purpose The Taiwan high-speed railway (THSR) system plays an important role in maintaining efficient transportation of passengers around Taiwan. However, the control mechanisms of THSR and the traditional railway systems are quite different. Drivers on THSR-trains cannot control the cars by themselves; only the control center of THSR can give the commands, which are based on the train timetables and should be followed by the drivers to operate the cars. Moreover, when a disaster occurs, the control center needs to prepare a rescheduled timetable in accordance with current situations that drivers can follow. Method This study presents a methodology to esta lish a set of optimal operation rules which are tree-based rules for real-time train timetable control for the THSR-system. The rules can be used to determine the optimal real-time operation during disturbances. Steps of the proposed methodology involve: (i) building of train timetable optimization model, (ii) generation of optimal input-output patterns, and (iii) extraction of tree-based rules for designed scenarios using the decision-tree algorithm. Results & Discussion The model could generate a timetable result that was as good as a real timetable. This means it has potential as a simulation analysis for predicting the effect of disruptions on the timetable without doing the real experiment with train timetables during disruptive events.

A divide and conquer-based greedy search for two-machine no-wait job shop problems with makespan minimisation

This paper addresses a two-machine no-wait job shop problem with makespan minimisation. It is well known that this problem is strongly NP-hard. A divide-and-conquer approach (DC for short) is adopted to calculate the optimal timetable of a given sequence. It decomposes the given sequences into several independent parts and conquers them separately. A timetable enhancing method is introduced to further improve the timetable obtained by DC. It constructs a set of flow shop type jobs based on the result from DC and calculates the best timetable for these newly constructed jobs by the well-known Gilmore and Gomory method (GG for short). An efficient greedy search is proposed by integrating DC with GG to search for the best sequence. Experimental results show that the proposed algorithm can find the optimal solutions for 96% of the randomly generated test instances on average.

Optimal Scheduling of Track Maintenance on a Railway Network

To ensure the safety and continued operation of the railway network system, many maintenance and renewal activities are performed on the track every month. Unplanned maintenance activities are expensive and would cause low service quality. Therefore, the track condition should be monitored, and when it has degraded beyond some acceptable limit, it should be scheduled for maintenance before failure. An optimal timetable of the maintenance activities is needed to be scheduled, planning the monthly workload, to reduce the effect on the transportation service and to reduce the potential costs. Considering the uncertainties of the deterioration process, the safety of transportation service, the lifetime loss of the replaced track, the maintenance cost and the travel cost, this article advances an optimisation model for the maintenance scheduling of a regional railway network. An enhanced genetic algorithm approach is proposed to search for a solution producing maintenance schedule such that the overall cost is minimised in a finite planning horizon. A case study is given to demonstrate the application of the method. The case study results were derived by using an enhanced genetic algorithm method, which is specifically developed to deal with the characteristics of the railway maintenance problem. Copyright © 2012 John Wiley & Sons, Ltd.

Fuzzy optimal schedule of high speed train operation to minimize energy consumption with uncertain delays and driver's behavioral response

Energy efficiency is an important concern in for railway administrations and operators. Strategies focused on traffic operation can achieve energy savings in short term and with associated low investments. For that purpose the main strategies are the design of efficient timetables and driving (ecodriving). The ecodriving applies coasting commands (null traction force) to reduce energy consumption, taking into account downhill slopes, speed reductions, etc. (Acikbas and Soylemez, 2008). However, timetable models in literature do not typically consider energy minimization as a goal, and punctuality requirements under uncertainty. In this paper a model for the joint design of ecodriving and timetable under uncertainty for high speed lines is proposed where the railway operator and administrator requirements are incorporated. Uncertainty in delays is modeled as fuzzy numbers and punctuality constraints, and the timetable optimization model is a fuzzy linear programming model, in which the objective function includes the consumptions of delayed scenarios and the behavioral response of the driver that will affect the consumption. The ecodriving design is based on a Genetic Algorithm that makes use of a detailed simulation model, taking into account the specific characteristics of high speed lines and trains. The proposed method is applied to a real Spanish high speed line to optimize the operation and it is compared to the current commercial service in order to evaluate the potential energy savings.

On Multi-Start Algorithms for Optimization of High School Timetables

The paper deals with the problem of high-school time-tabling that is important in applications, but hard for solving. The algorithm is presented for timetabling based on Multi-start and Simulated Annealing with parameters adapted using the Bayes approach. The algorithm proposed is compared with other timetabling algorithms using the web-based software. A multi-start algorithm is a simple way to provide the convergence, if the number of uniformly distributed starting points is large. A disadvantage is slow convergence.Therefore, the first aim of this paper is experimental comparisons of the efficiency of different versions of multi-start algorithms in the optimization of timetables. To obtain representative results, the algorithms should be compatible with the Lithuanian high school practice and flexible enough for adaptation to different high schools.The second aim is a web-based implementation of these algorithms in a way convenient for high schools. The web-based software is important for evaluation and comparison of algorithms by independent experts, as well, since the efficiency of algorithms depends on subjective parameters specific to each school, so on-line calculations are needed to obtain representative data. It is useful for scientific cooperation and applications to different schools. In addition, the software for evaluating of real timetables is included to compare with the results of optimization.

Existence of a trade-off factorization of a partially 4-homogeneous graph

We consider a graph G with 2κ vertices of degree 5 and κ vertices of degree 2, all other vertices being of degree 4. In connection with the timetable optimization problem, we study necessary and sufficient conditions for the existence of a factorization of G into two skeleton subgraphs whose edge sets are disjoint and have the same cardinality and, for each vertex of the graph, the numbers of edges incident to this vertex in these subgraphs differ at most by unity.

Recoverable Robust Timetables: An Algorithmic Approach on Trees

In the context of scheduling and timetabling, we study a challenging combinatorial problem which is very interesting for both practical and theoretical points of view. The motivation behind it is to cope with scheduled activities which might be subject to unavoidable disruptions, such as delays, occurring during the operational phase. The idea is to preventively plan some extra time for the scheduled activities in order to be "prepared” if a delay occurs, and absorb it without the necessity of rescheduling all the activities from scratch. This realizes the concept of designing robust timetables. During the planning phase, one should also consider recovery features that might be applied at runtime if disruptions occur. This leads to the concept of recoverable robust timetables. In this new concept, it is assumed that recovery capabilities are given as input along with the possible disruptions that must be considered. The main objective is the minimization of the overall needed time. The quality of a robust timetable is measured by the price of robustness, i.e., the ratio between the cost of the robust timetable and that of a nonrobust optimal timetable. We show that finding an optimal solution for this problem is NP-hard even though the topology of the network, which models dependencies among activities, is restricted to trees. However, we manage to design a paeudopolynomial time algorithm based on dynamic programming and apply it on both random networks and real case scenarios provided by Italian railways. We evaluate the effect of robustness on the scheduling of the activities and provide the price of robustness with respect to different scenarios. We experimentally show the practical effectiveness and efficiency of the proposed algorithm.

Methods and time schedule for follow-up of intracranial aneurysms treated with endovascular embolization: a systematic review

Background and purposeTo review the diagnostic value of angiographic methods and the optimal timetable for follow-up imaging of patients after endovascular treatment of intracranial aneurysms. Material and methodsA comprehensive computer-aided search for relevant primary papers was performed using the MEDLINE, PubMed, Embase, and Cochrane Collaboration database from January 1991 to March 2011. Original papers were included that reported either diagnostic value of angiographic modalities for follow-up vs. digital subtracted angiography (DSA) or comparison of aneurysm occlusion rate in delayed vs. early follow-up. ResultsThe systematic review identified 35 relevant studies: 3 on the diagnostic value of three-dimensional (3D) DSA, 30 on the performance of magnetic resonance angiography (MRA), and 3 on time schedules for follow-up. 3D DSA had sensitivity of 100%, and specificity of 58.3-94.7%. Magnetic resonance angiography had sensitivity of 28.4-100%, and specificity of 50.0-100%. The proportion of aneurysms that recanalized between the early follow-up examination at 6 months and the delayed imaging at 1.5-6.0 years was 0-2.5%. ConclusionsMagnetic resonance angiography seems to be the best imaging method for the follow-up. In selected cases, when invasive angiography is necessary, 3D DSA should be considered to improve the diagnostic accuracy. Most patients who present with stable and adequate aneurysm occlusion at 6 months after coiling may not require further follow-up.

An activity-based approach for scheduling multimodal transit services

This paper proposes a new activity-based transit assignment model for investigating the scheduling (or timetabling) problem of transit services in multi-modal transit networks. The proposed model can be used to generate the short-term and long-term timetables of multimodal transit lines for transit operations and service planning purposes. The interaction between transit timetables and passenger activity-travel scheduling behaviors is captured by the proposed model, as the activity and travel choices of transit passengers are considered explicitly in terms of departure time choice, activity/trip chain choices, activity duration choice, transit line and mode choices. A heuristic solution algorithm which combines the Hooke–Jeeves method and an iterative supply–demand equilibrium approach is developed to solve the proposed model. Two numerical examples are presented to illustrate the differences between the activity-based approach and the traditional trip-based method, together with comparison on the effects of optimal timetables with even and uneven headways. It is shown that the passenger travel scheduling pattern derived from the activity-based approach is significantly different from that obtained by the trip-based method, and that a demand-sensitive (with uneven headway) timetable is more efficient than an even-headway timetable.

EClasSkeduler: A Course Scheduling System for the Executive Education Unit at the Universidad de Chile

Each October, the Executive Education Unit at the Universidad de Chile develops its course schedules for the following year. By 2008, the complexities of increasing enrollments and course offerings had rendered its manual timetabling process unmanageable. Inconvenient and inflexible scheduling decisions were causing discontent among instructors and students, making the need for a more efficient system of assigning classrooms patent. Three characteristics distinguish the unit's situation from the classic university course timetabling problem. First, its courses vary in duration, ranging between 15 and 30 weeks. Second, its course start dates are spread over the academic year. Finally, each course's start date is flexible and must fall within a window defined by the earliest and latest start dates. This paper presents an automated computational system that generates optimal timetables and classroom assignments for all the unit's courses, minimizing both operating costs and schedule conflicts. When we compared the schedules it generated with the unit's manually generated timetables, we found that our system yielded average cost savings of 35 percent; in addition, it reduced execution times (for generating schedules) from two weeks to less than 30 minutes.

Optimization of transit route network, vehicle headways and timetables for large-scale transit networks

This paper presents a metaheuristic method for optimizing transit networks, including route network design, vehicle headway, and timetable assignment. Given information on transit demand, the street network of the transit service area, and total fleet size, the goal is to identify a transit network that minimizes a passenger cost function. Transit network optimization is a complex combinatorial problem due to huge search spaces of route network, vehicle headways, and timetables. The methodology described in this paper includes a representation of transit network variable search spaces (route network, headway, and timetable); a user cost function based on passenger random arrival times, route network, vehicle headways, and timetables; and a metaheuristic search scheme that combines simulated annealing, tabu, and greedy search methods. This methodology has been tested with problems reported in the existing literature, and applied to a large-scale realistic network optimization problem. The results show that the methodology is capable of producing improved solutions to large-scale transit network design problems in reasonable amounts of time and computing resources.

TSL Dissertation Abstracts—2006 Transportation Science and Logistics Society Dissertation Prize Competition

The Transportation Science and Logistics (TSL) Society Dissertation Prize Competition is the oldest and most prestigious competition for doctoral dissertations in the field. The 2006 TSL dissertation prize committee consisted of Professor Michel Bierlaire (École Polytechnique Fédérale de Lausanne), Professor Ann Campbell (University of Iowa), Professor Alan Erera (Georgia Institute of Technology), Professor Donald Hearn (University of Florida), and Professor Mark Hickman (University of Arizona). Eligibility was limited to doctoral dissertations completed between June 1, 2005, and May 31, 2006, in the general area of transportation science and logistics. To be considered, a dissertation must have been nominated by the author’s thesis supervisor. This year we received 26 nominations from 24 universities and 10 countries, representing such diverse areas as vehicle routing, vehicle scheduling, traveler behavior, activity analysis, logistics, and supply chain management. This year’s pool of dissertations was exceptional in both its breadth and depth, showing remarkable theoretical and practical insights into many very interesting problems in transportation and logistics. With the large number of submissions and their exceptional quality, it was not easy for the committee to select a first place winner and an honorable mention. I would like to thank the authors, their advisors, and the prize committee for their part in this effort to recognize and honor the field’s outstanding doctoral researchers. Awards were announced at the TSL meeting at the 2006 INFORMS meeting in Pittsburgh. Perhaps without saying, the theses nominated for the TSL Dissertation Prize are distinguished by the fact that they were nominated for the award. Each dissertation makes a unique and valuable contribution to transportation science and logistics, and all entrants and their advisors deserve our sincere congratulations. Abstracts for the 26 dissertations follow; awardees are listed first, and finalists’ abstracts follow in alphabetical order by author. First Place: Christian Liebchen, Technische Universität Berlin, Germany. Advisors: Rolf H. Möhring and Karl Nachtigall. Title: “Periodic Timetable Optimization in Public Transport”. Honorable Mention: Anne Goodchild, University of California, Berkeley. Advisor: Carlos Daganzo. Title: “Crane Double Cycling in Container Ports: Algorithms, Evaluation, and Planning”.

A three-phase approach for operating theatre schedules

In this paper we develop a three-phase, hierarchical approach for the weekly scheduling of operating rooms. This approach has been implemented in one of the surgical departments of a public hospital located in Genova (Genoa), Italy. Our aim is to suggest an integrated way of facing surgical activity planning in order to improve overall operating theatre efficiency in terms of overtime and throughput as well as waiting list reduction, while improving department organization. In the first phase we solve a bin packing-like problem in order to select the number of sessions to be weekly scheduled for each ward; the proposed and original selection criterion is based upon an updated priority score taking into proper account both the waiting list of each ward and the reduction of residual ward demand. Then we use a blocked booking method for determining optimal time tables, denoted Master Surgical Schedule (MSS), by defining the assignment between wards and surgery rooms. Lastly, once the MSS has been determined we use the simulation software environment Witness 2004 in order to analyze different sequencings of surgical activities that arise when priority is given on the basis of a) the longest waiting time (LWT), b) the longest processing time (LPT) and c) the shortest processing time (SPT). The resulting simulation models also allow us to outline possible organizational improvements in surgical activity. The results of an extensive computational experimentation pertaining to the studied surgical department are here given and analyzed.

STABILITY EVALUATION OF A RAILWAY TIMETABLE AT THE STATION LEVEL

This study deals with a real-world planning problem in railroad infrastructure operations. The research was done as part of the RECIFE project, which is working on a decision support software designed to evaluate junction or station capacity. One of the aims of the RECIFE project is to develop a timetable optimization model as well as timetable evaluation modules. This paper presents a module for evaluating timetable stability based on an original method using shortest path problem resolution. An example involving the Pierrefitte-Gonesse junction is also presented.

A Lagrangian heuristic algorithm for a real-world train timetabling problem

The train timetabling problem (TTP) aims at determining an optimal timetable for a set of trains which does not violate track capacities and satisfies some operational constraints. In this paper, we describe the design of a train timetabling system that takes into account several additional constraints that arise in real-world applications. In particular, we address the following issues: • Manual block signaling for managing a train on a track segment between two consecutive stations. • Station capacities, i.e., maximum number of trains that can be present in a station at the same time. • Prescribed timetable for a subset of the trains, which is imposed when some of the trains are already scheduled on the railway line and additional trains are to be inserted. • Maintenance operations that keep a track segment occupied for a given period. We show how to incorporate these additional constraints into a mathematical model for a basic version of the problem, and into the resulting Lagrangian heuristic. Computational results on real-world instances from Rete Ferroviaria Italiana (RFI), the Italian railway infrastructure management company, are presented.

The demand-dependent optimization of regular train timetables

Abstract Regular timetables, in which the trains arrive and depart at constant intervals, have been adopted in various European countries, because of the simpler and fairer service they allow. The design of such a timetable has recently received a certain attention in the literature. This paper extends the commonly adopted model to take into account the reciprocal influence between the quality of a timetable and the transport demand captured by the railway with respect to alternative means of transport. The resulting mixed-integer non linear model remains non convex even after relaxing the integrality constraints. We solve it by a branch-and-bound algorithm based on Outer Approximation and a heuristic algorithm exploiting the decomposition and reciprocal update of two submodels. Preliminary computational results concern a regional network in North-western Italy.

A genetic algorithm for a university weekly courses timetabling problem

The timetabling problem is concerned with the allocation, subject to constraints, of given resources to objects in space and time in such way as to satisfy as nearly as possible a set of desirable objectives. This problem is known to be NP–complete and as such only combinatorial optimization methods can guarantee an optimal timetable. In this paper we propose a sector–based genetic algorithm for solving a university weekly courses timetabling problem. Preliminary experimental results indicate that the algorithm is promising.

Optimal timetables for public transportation

This paper analyzes the optimal timetable for a given number of public transport vehicles on a single transit line when riders differ with respect to the times at which they prefer to travel and the schedule delay costs they incur from traveling earlier or later than desired. The problem of minimizing riders' total schedule delay costs is formulated in continuous time and first-order optimality conditions are identified. An explicit solution is derived for the “line” model in which preferred travel times are uniformly distributed in the population over part of the day and trips cannot be rescheduled between days. This solution is compared with the optimal schedule for the “circle” model in which preferred travel times are uniformly distributed over the full 24 h day and trips can be rescheduled between days.

Optimization Criteria for Public Transportation Services

Abstract This paper describes precise criteria for public transportation services which can be used for (automated) time table optimization. All proposed evaluations are normalized to compare different trips and sets of routes even between different transport systems. The proposed functions are applied to an example with a periodic train schedule.