Polytopes related to interval vectors and incidence matrices

AbstractIn this short note we investigate polytopes associated with families of interval vectors, i.e., (0,1)-vectors with consecutive ones. Using a linear transformation we show a connection to “extended” incidence matrices of acyclic directed graphs and the convex hull of their columns. This leads to complete linear descriptions of the corresponding polytopes

Offline Scheduling of Map and Reduce Tasks on Hadoop Systems

International audienceMapReduce is a model to manage quantities massive of data. It is based on the distributed and parallel execution of tasks over the cluster of machines. Hadoop is an implementation of MapReduce model, it is used to offer BigData services on the cloud. In this paper, we expose the scheduling problem on Hadoop systems. We focus on the offline-scheduling, expose the problem in a mathematic model and use the time-indexed formulation. We aim consider the maximum of constraints of the MapReduce environment. Solutions for the presented model would be a reference for the on-line Schedules in the case of low and medium instances. Our work is useful in term of the problem definition: constraints are based on observations and take into account resources consumption, data locality, heterogeneous machines and workflow management; this paper defines boundaries references to evaluate the online model

A two-stage dynamic model on allocation of construction facilities with genetic algorithm

Author name used in this publication: K. W. Chau2003-2004 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

A two-stage dynamic model on allocation of construction facilities with genetic algorithm

By their very nature, activities within the construction site are generally highly dynamic and complex. Hence, it is highly desirable to be able to formulate the optimal strategy for allocating site-level facilities at different times of the project. The principal objective is to minimize the total cost, which comprises the transportation, handling, capital, and operating costs at potential intermediate transfer centers of various plant and material resources over the entire project duration. The problem can be formulated as a mixed integer program, which entails enormous computational effort for the solution, in particular when the problem size is large. In this paper, a two-stage dynamic model is developed to assist construction planners to formulate the optimal strategy for establishing potential intermediate transfer centers for site-level facilities such as batch plants, lay-down yards, receiving warehouses, various workshops, etc. Under this approach, the solution of the problem is split into two stages, namely, a lower-level stage and an upper-level stage. The former can be solved by a standard linear programming method, whereas the latter is solved by a genetic algorithm. The efficiency of the proposed algorithm is demonstrated through case examples.Department of Civil and Environmental EngineeringAuthor name used in this publication: K. W. Cha

Minimización del tiempo total de flujo de tareas en una sola máquina: Estado del arte

La programación de operaciones en una sola máquina es un problema clásico de la investigación de operaciones. Numerosos métodos han sido propuestos para resolver diferentes instancias del problema, dependiendo de las restricciones impuestas y del objetivo del mismo. En este artículo estamos interesados en ilustrar el estado actual de desarrollo de los métodos y algoritmos existentes en la literatura para el problema de minimización del flujo total de tareas sujetas a fechas de llegadas, tanto en problemas estáticos como dinámicos. Además, las posibilidades de trabajo y las preguntas abiertas serán igualmente expuestas

The Tick Formulation for deadlock detection and avoidance in railways traffic control

Wrong dispatching decisions may lead to deadlocks, where trains reciprocally block resources necessary to reach their destinations. It is crucial to develop tools to detect such potential deadlocks on time, in order to reverse the decisions previously taken by dispatchers or to take recovery actions. In this paper we present a new 0,1 linear formulation for detecting deadlocks and optimally park the involved trains to reduce congestion around the affected area. We discuss computational results on some realistic randomly generated instances to show the validity of the approach, as well as its limits.acceptedVersio

Single Machine Scheduling with Release Dates

We consider the scheduling problem of minimizing the average weighted completion time of n jobs with release dates on a single machine. We first study two linear programming relaxations of the problem, one based on a time-indexed formulation, the other on a completiontime formulation. We show their equivalence by proving that a O(n log n) greedy algorithm leads to optimal solutions to both relaxations. The proof relies on the notion of mean busy times of jobs, a concept which enhances our understanding of these LP relaxations. Based on the greedy solution, we describe two simple randomized approximation algorithms, which are guaranteed to deliver feasible schedules with expected objective value within factors of 1.7451 and 1.6853, respectively, of the optimum. They are based on the concept of common and independent a-points, respectively. The analysis implies in particular that the worst-case relative error of the LP relaxations is at most 1.6853, and we provide instances showing that it is at least e/(e - 1) 1.5819. Both algorithms may be derandomized, their deterministic versions running in O(n2 ) time. The randomized algorithms also apply to the on-line setting, in which jobs arrive dynamically over time and one must decide which job to process without knowledge of jobs that will be released afterwards