Performance measure of a multi-state flow network under reliability and maintenance cost considerations

In this paper, each edge in a multi-state flow network is characterized by both multi-valued capacities and a maintenance cost. Accordingly, the performance of a multi-state flow network is measured by capacity reliability as well as maintenance budget limit. An integrated performance indicator MR(d,b) is defined as the probability that a multi-state flow network can provide the required capacity level d while satisfying the maintenance budget limit b. An algorithm is developed to calculate MR(d,b) exactly. Unlike the exhaustive algorithm that enumerates each capacity vector one by one, the developed algorithm iteratively separates capacity vectors satisfying the required capacity level d from the universal space, and then checks whether they meet the maintenance budget limit b. Furthermore, the efficiency of the developed algorithm is validated via numerical experiments.

Automated summary

This paper introduces a comprehensive performance indicator to measure the performance of multi-state flow networks, along with an algorithm to calculate this indicator. The algorithm iteratively separates capacity vectors and checks maintenance budget limits to improve efficiency, which is validated through numerical experiments.