Calcul exact de la disponibilité opérationnelle d'un système complexe
In this article we present a generalization of Markov Decision Processes with discreet time where the immediate rewards in every period are not deterministic but random, with the two first moments of the distribution given.Formulas are developed to calculate the expected value and the variance of the reward of the process, formulas which generalize and partially correct other results. We make some observations about the distribution of rewards for processes with limited or unlimited horizon and...
En este artículo se estudia el problema de determinar la función de distribución del tiempo de vida de las componentes de un sistema binario, a partir del conocimiento de las leyes que rigen el funcionamiento del sistema y del conjunto de componentes que causa su fallo (obtenida mediante autopsia del sistema en el momento de su deterioro).Se presentan los resultados de Meilijson (1981) y Nowik (1990) que proponen un sistema de ecuaciones implícito para obtener estas distribuciones. Sin embargo,...
Este artículo expone un método para el cálculo del número medio de máquinas en funcionamiento en un sistema formado por un operario y N máquinas iguales, con tiempos exponenciales de funcionamiento entre averías y tiempos de servicio aleatorios, idéntica e independientemente distribuidos. El modelo generaliza las conocidas fórmulas que se obtienen a partir de los modelos M/M/1 con centro emisor finito y de Ashcroft, que suelen utilizarse para el problema de asignación de máquinas.
We consider point sets in (Z^2,n) where no three points are on a line – also called caps or arcs. For the determination of caps with maximum cardinality and complete caps with minimum cardinality we provide integer linear programming formulations and identify some values for small n.
Las propiedades geométricas del conjunto factible del dual de un problema semiinfinito lineal son análogas a las correspondientes para el caso finito. En este trabajo mostramos cómo, a partir de la caracterización algebraica de vértices y direcciones extremas, se consigue la correspondiente para aristas infinitas, estableciéndose así las bases para una extensión del método simplex a programas semiinfinitos lineales.
In this work, we introduce a new software created to study hematopoiesis at the cell population level with the individually based approach. It can be used as an interface between theoretical works on population dynamics and experimental observations. We show that this software can be useful to study some features of normal hematopoiesis as well as some blood diseases such as myelogenous leukemia. It is also possible to simulate cell communication and the formation of cell colonies in the bone marrow. ...
In the course of globalization, many enterprises change their strategies and are coupled in partnerships with suppliers, subcontractors and customers. This coupling forms supply chains comprising several geographically distributed production facilities. Production planning in a supply chain is a complicated and difficult task, as it has to be optimal both for the local manufacturing units and for the whole supply chain network. In this paper two analytical models are used to solve the production planning...
This paper considers a variant of the bottleneck transportation problem. For each supply-demand point pair, the transportation time is an independent random variable. Preference of each route is attached. Our model has two criteria, namely: minimize the transportation time target subject to a chance constraint and maximize the minimal preference among the used routes. Since usually a transportation pattern optimizing two objectives simultaneously does not exist, we define non-domination in this...
In this paper, we are concerned with a civil engineering application of optimization, namely the optimal design of a loaded beam. The developed optimization model includes ODE-type constraints and chance constraints. We use the finite element method (FEM) for the approximation of the ODE constraints. We derive a convex reformulation that transforms the problem into a linear one and find its analytic solution. Afterwards, we impose chance constraints on the stress and the deflection of the beam....
We explore reformulation of nonlinear stochastic programs with several joint chance constraints by stochastic programs with suitably chosen penalty-type objectives. We show that the two problems are asymptotically equivalent. Simpler cases with one chance constraint and particular penalty functions were studied in [6,11]. The obtained problems with penalties and with a fixed set of feasible solutions are simpler to solve and analyze then the chance constrained programs. We discuss solving both problems...