Reliability evaluation of network flows with stochastic capacity and cost constraint. (English) Zbl 1390.90106

Fathabadi, H. Salehi; Khodaei, M.

Int. J. Math. Oper. Res. 4, No. 4, 439-452 (2012).

Summary: This paper addresses flow networks whose arcs have finite and independent random capacities. The reliability of such a system, that is the probability that \(d\) units of flow can be transmitted from the source node to the sink node with total cost at most equal to \(c\), can be computed in terms of Minimal Path Vectors, named as \((d,c)\)-MPs. In this paper, first, a method for computing the upper and lower bounds of the capacity cost of the system is proposed. The presented method shows how to compute a \((d,c)\)-MP with the minimum capacity cost. Subsequently, we develop an algorithm, based on the computed bounds, to generate all \((d,c)\)-MPs and then, the system reliability is calculated in terms of such \((d,c)\)-MPs. The computational complexity of the proposed algorithm is also presented. At the end the solution procedure is illustrated by an example.

MSC:

90B10	Deterministic network models in operations research
90B25	Reliability, availability, maintenance, inspection in operations research

Keywords:

reliability evaluation; stochastic network flows; minimal path; algorithm complexity