ATMOS 2005 Abstracts Collection -- Selected Papers from the 5th Workshop on Algorithmic Methods and Models for Optimization of Railways

This issue contains six papers that were presented in preliminary form at the 5th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS 2005), held at Palma de Mallorca, Spain, October 7, 2005 in conjunction with ALGO 2005. These papers are representative of several areas of research within the scope of ATMOS: rolling stock circulation and engine assignment, station location, line planning, railway traffic scheduling and dispatching, transfer optimization within network design, and fast traffic information systems

Optimising halting station of passenger railway lines

In many real life passenger railway networks, the types of stations and lines characterisethe halting stations of the train lines. Common types are Regional, Interregional or Intercity.This paper considers the problem of altering the halts of lines by both upgrading and downgrading stations, such that this results in less total travel time. We propose a combination of reduction methods, Lagrangian relaxation, and a problem-specific multiplier adjustment algorithm to solve the presented mixed integer linear programming formulation. A computational study of several real-life instances based on problem data of the Dutch passenger railway operator NS Reizigers is included.mathematical economics and econometrics ;

Returnable containers: an example of reverse logistics

Considers the application of returnable containers as an example of reverse logistics. A returnable container is a type of secondary packaging that can be used several times in the same form, in contrast with traditional cardboard boxes. For this equipment to be used, a system for the return logistics of the containers should be available: this system should guarantee that the containers are transported from the recipients to the next senders, and that they are cleaned and maintained, if necessary. Outlines several ways in which the return of these containers can be organized. Also includes a case study involving the design of such a return logistic system in The Netherlands. Also describes a quantitative model that can be used to support the related planning process

License class design: complexity and algorithms

In this paper a generalization of the Fixed Job Scheduling Problem (FSP) is considered, which appears in the aircraft maintenance process at an airport. A number of jobs have to be carried out, where the main attributes of a job are a fixed start time, a fixed finish time and an aircraft type. For carrying out these jobs a number of engineers are available. An engineer is allowed to carry out a specific job only if he has a license for the corresponding aircraft type. Furthermore, the jobs must be carried out in a non-preemptive way and each engineer can be carrying out at most one job at the same time. Within this setting natural questions to be answered ask for the minimum number of engineers required for carrying out all jobs or, more generally, for the minimum total costs for hiring engineers. In this paper a complete classification of the computational complexity of two classes of mathematical problems related to these practical questions is given. Furthermore, it is shown that the polynomially solvable cases of these problems can be solved by a combination of Linear Programming and Network Flow algorithms

An analysis of shift class design problems

In this paper we consider a generalization of the Fixed Job Schedule Problem (FJSP) which appears in the aircraft maintenance process at an airport. A number of jobs must be carried out where each job requires processing from a fixed time to a fixed finish time. These jobs must be carried out by a number of machines which are available in specific shifts only. The jobs must be carried out in a non-preemptive way, although at the end of a shift preemption of a job is allowed sometimes. The problem is to choose the number of machines in each of the shifts in such a way that all jobs can be carried out and that the total costs of the machines or the total number of machines are minimum. In this paper we present an analysis of the computational complexity of these problems. We also analyse the worst case behaviour of the preemptive variant versus the non-preemptive variant

On the computational complexity of (maximum) shift class scheduling

In this paper we consider a generalization of the Fixed Job Scheduling Problem (FSP) which appears in a natural way in the aircraft maintenance process at an airport. A number of jobs has to be carried out, where the main attributes of a job are: a fixed start time, a fixed finish time and a value representing the priority of the job. For carrying out these jobs a number of machines is available. These machines are available in specific time intervals (shifts) only. A job can be carried out by a machine only if the interval between the start time and the finish time of the job is a subinterval of the shift of the machine. Furthermore, the jobs must be carried out in a non-preemptive way and each machine can be carrying out at most one job at the same time

On the computational complexity of (maximum) class scheduling

In this paper we consider several generalizations of the Fixed Job Scheduling Problem (FSP) which appear in a natural way in the aircraft maintenance process at an airport: A number of jobs have to be carried out, where the main attributes of a job are: a fixed start time, a fixed finish time, a value representing the job's priority and a job class. For carrying out these jobs a number of machines are available. These machines can be split up into a number of disjoint machine classes. For each combination of a job class and a machine class it is known whether or not it is allowed to assign a job in the job class to a machine in the machine class. Furthermore the jobs must be carried out in a non-preemptive way and each machine can be carrying out at most one job at the same time. Within this setting one can ask for a feasible schedule for all jobs or, if such a schedule does not exist, for a feasible schedule for a subset of the jobs of maximum total value. In this paper we present a complete classification of the computational complexity of two classes of combinatorial problems related this operational job scheduling problem

Mathematical models for planning support

In this paper we describe how computer systems can provide planners with active planning support, when these planners are carrying out their daily planning activities. This means that computer systems actively participate in the planning process by automatically generating plans or partial plans. Active planning support by computer systems requires the application of mathematical models and solution techniques. In this paper we describe the modeling process in general terms, as well as several modeling and solution techniques. We also present some background information on computational complexity theory, since most practical planning problems are hard to solve. We also describe how several objective functions can be handled, since it is rare that solutions can be evaluated by just one single objective. Furthermore, we give an introduction into the use of mathematical modeling systems, which are useful tools in a modeling context, especially during the development phases of a mathematical model. We finish the paper with a real life example related to the planning process of the rolling stock circulation of a railway operator

Algorithmic Support for Railway Disruption Management

Disruptions of a railway system are responsible for longer travel times and much discomfort for the passengers. Since disruptions are inevitable, the railway system should be prepared to deal with them effectively. This paper explains that, in case of a disruption, rescheduling the timetable, the rolling stock circulation, and the crew duties is so complex that solving them manually is too time consuming in a time critical situation where every minute counts. Therefore, algorithmic support is badly needed. To that end, we describe models and algorithms for real-time rolling stock rescheduling and real-time crew rescheduling that are currently being developed and that are to be used as the kernel of decision support tools for disruption management. Furthermore, this paper argues that a stronger passenger orientation, facilitated by powerful algorithmic support, will allow to mitigate the adverse effects of the disruptions for the passengers. The latter will contribute to an increased service quality provided by the railway system. This will be instrumental in increasing the market share of the public transport system in the mobility market

Companion based matrix functions: description and minimal factorization

Companion based matrix functions are rational matrix functions admitting a minimal realization involving state space matrices that are first companions. Necessary and sufficient conditions are given for a rational matrix function to be companion based. Minimal factorization of such functions is discussed in detail. It is shown that the property of being companion based is hereditary with respect to minimal factorization. Also, the issue of minimal factorization is reduced to a division problem for pairs of monic polynomials of the same degree. In this context, a connection with the Euclidean algorithm is made. The results apply to canonical Wiener-Hopf factorization as well as to complete factorization. The analysis of the latter leads to a combinatorial problem involving the eigenvalues of the state space matrices. The algorithmic aspects of this problem are intimately related to the two machine flow shop problem and Johnson's rule from job scheduling theory