In this paper, a stochastic problem of multicenter location on a graph was formulated through the modification of the existing p-center problem to determine the location of a given number of facilities, to maximize the reliability of supplying the system. The system is represented by a graph whose nodes are the locations of demand and the potential facilities, while the weights of the arcs represent the reliability, i.e., the probability that an appropriate branch is available. First, k locations of facilities are randomly determined. Using a modified Dijkstra’s algorithm, the elementary path of maximal reliability for every demand node is determined. Then, a graph of all of elementary paths for demand node is formed. Finally, a new algorithm for calculating the reliability of covering a node from k nodes (k—covering reliability) was formulated.
Abstract
In this paper, a stochastic problem of multicenter location on a graph was formulated through the modification of the existing p-center problem to determine the location of a given number of facilities, to maximize the reliability of supplying the system. The system is represented by a graph whose nodes are the locations of demand and the potential facilities, while the weights of the arcs represent the reliability, i.e., the probability that an appropriate branch is available. First, k locations of facilities are randomly determined. Using a modified Dijkstra’s algorithm, the elementary path of maximal reliability for every demand node is determined. Then, a graph of all of elementary paths for demand node is formed. Finally, a new algorithm for calculating the reliability of covering a node from k nodes (k—covering reliability) was formulated.