Minimization of the Expected Total Net Loss in a Stationary Multistate Flow Network System  

作　　者：Kristina Skutlaberg Bent Natvig Kristina Skutlaberg;Bent Natvig(Department of Mathematics, University of Oslo, Oslo, Norway)

机构地区：[1]Department of Mathematics, University of Oslo, Oslo, Norway

出　　处：《Applied Mathematics》2016年第8期793-817,共25页应用数学（英文）

摘　　要：In the present paper, a three-component, stationary, multistate flow network system is studied. Detailed costs and incomes are specified. The aim is to minimize the expected total net loss with respect to the expected times the components spend in each state. This represents a novelty in that we connect the expected component times spent in each state to the minimal total net loss of the system, without first finding the component importance. This is of interest in the design phase where one may tune the components to minimize the expected total net loss. Due to the complex nature of the problem, we first study a simplified version. There the expected times spent in each state are assumed equal for each component. Then a modified version of the full model is presented. The optimization in this model is completed in two steps. First the optimization is carried out for a set of pre-chosen fixed expected life cycle lengths. Then the overall minimum is identified by varying these expectations. Both the simplified and the modified optimization problems are nonlinear. The setup used in this article is such that it can easily be modified to represent other flow network systems and cost functions. The challenge lies in the optimization of real life systems.In the present paper, a three-component, stationary, multistate flow network system is studied. Detailed costs and incomes are specified. The aim is to minimize the expected total net loss with respect to the expected times the components spend in each state. This represents a novelty in that we connect the expected component times spent in each state to the minimal total net loss of the system, without first finding the component importance. This is of interest in the design phase where one may tune the components to minimize the expected total net loss. Due to the complex nature of the problem, we first study a simplified version. There the expected times spent in each state are assumed equal for each component. Then a modified version of the full model is presented. The optimization in this model is completed in two steps. First the optimization is carried out for a set of pre-chosen fixed expected life cycle lengths. Then the overall minimum is identified by varying these expectations. Both the simplified and the modified optimization problems are nonlinear. The setup used in this article is such that it can easily be modified to represent other flow network systems and cost functions. The challenge lies in the optimization of real life systems.

关 键 词：RELIABILITY Nonlinear Optimization Multistate Flow Network 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]