TITLE:
Minimization of the Expected Total Net Loss in a Stationary Multistate Flow Network System
AUTHORS:
Kristina Skutlaberg, Bent Natvig
KEYWORDS:
Reliability, Nonlinear Optimization, Multistate Flow Network
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.8,
May
24,
2016
ABSTRACT: 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.