Polygon scheduling

Consider a set of circles of the same length and r irregular polygons with vertices on a circle of this length. Each of the polygons has to be arranged on a given subset of all circles and the positions of the polygon on the different circles are depending on each other. How should the polygons be arranged relative to each other to minimize some criterion function depending on the distances between adjacent vertices on all circles? A decomposition of the set of all arrangements of the polygons into local regions in which the optimization problem is convex is given. An exact description of the local regions and a sharp bound on the number of local regions are derived. For the criterion functions minimizing the maximum weighted distance, maximizing the minimum weighted distance, and minimizing the sum of weighted distances the local optimization problems can be reduced to polynomially solvable network flow problems

An Overview and Categorization of Approaches for Train Timetable Generation

A train timetable is a crucial component of railway transportation systems as it directly impacts the system’s performance and the customer satisfaction. Various approaches can be found in the literature that deal with timetable generation. However, the approaches proposed in the literature differ significantly in terms of the use case for which they are in tended. Differences in objective function, timetable periodicity, and solution methods have led to a confusing number of works on this topic. Therefore, this paper presents a com pact literature review of approaches to train timetable generation. The reviewed papers are briefly summarized and categorized by objective function and periodicity. Special emphasis is given to approaches that have been applied to real-world railway data

Periodic multiprocessor scheduling

A number of scheduling and assignment problems are presented involving the execution of periodic operations in a multiprocessor environment. We consider the computational complexity of these problems and propose approximation algorithms for operations with identical periods as well as for operations with arbitrary integer periods

Periodic multiprocessor scheduling

A number of scheduling and assignment problems are presented involving the execution of periodic operations in a multiprocessor environment. We consider the computational complexity of these problems and propose approximation algorithms for operations with identical periods as well as for operations with arbitrary integer periods

An Optimization Approach to a Geometric Packing Problem

We investigate several geometric packing problems (derived from an industrial setting) that involve fitting patterns of regularly spaced disks without overlap. We first derive conditions for achieving the feasible placement of a given set of patterns and construct a network formulation that, under certain conditions, allows the calculation of such a placement. We then discuss certain related optimization problems (e.g., fitting together the maximum number of patterns) and broaden the field of application by showing a connection to the well-known Periodic Scheduling Problem. In addition, a variety of heuristics are developed for solving large-scale instances of these provably difficult packing problems. The results of extensive computational testing, conducted on these heuristics, are presented

Schedule optimisation for cyclic tugger train systems

Es wird ein Modell präsentiert, durch welches getaktete Routenzugsysteme mit statischen Routen operativ geplant werden können. Zwei mathematische Optimierungsprobleme bilden die Kernergebnisse dieser Arbeit, mithilfe derer einsatzoptimaler Routenzugfahrpläne generiert werden können. Für das entwickelte Gesamtplanungsmodell zur Takt- und Fahrplanplanung werden optimale Lösungsverfahren präsentiert und anhand zweier Anwendungsfälle aus der Automobilindustrie evaluiert.This dissertation suggests a model to generate cyclic tugger train schedules with static routes within the operational logistics planning. Two mathematical optimization problems form the core results of this dissertation which allow the generation of non-overlapping schedules which can be carried out with a minimum number of tugger trains. To solve the overall planning model for cycle time and timetable planning, an optimal solution algorithm is presented and evaluated using two applications from the automotive industry

A Methodology for Transforming Java Applications Towards Real-Time Performance

The development of real-time systems has traditionally been based on low-level programming languages, such as C and C++, as these provide a fine-grained control of the applications temporal behavior. However, the usage of such programming languages suffers from increased complexity and high error rates compared to high-level languages such as Java. The Java programming language provides many benefits to software development such as automatic memory management and platform independence. However, Java is unable to provide any real-time guarantees, as the high-level benefits come at the cost of unpredictable temporal behavior.This thesis investigates the temporal characteristics of the Java language and analyses several possibilities for introducing real-time guarantees, including official language extensions and commercial runtime environments. Based on this analysis a new methodology is proposed for Transforming Java Applications towards Real-time Performance (TJARP). This method motivates a clear definition of timing requirements, followed by an analysis of the system through use of the formal modeling languageVDM-RT. Finally, the method provides a set of structured guidelines to facilitate the choice of strategy for obtaining real-time performance using Java. To further support this choice, an analysis is presented of available solutions, supported by a simple case study and a series of benchmarks.Furthermore, this thesis applies the TJARP method to a complex industrialcase study provided by a leading supplier of mission critical systems. Thecase study proves how the TJARP method is able to analyze an existing and complex system, and successfully introduce hard real-time guaranteesin critical sub-components