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.
Highlights
The problems of location include the tasks of selecting several facilities from a set of existing facilities, or determining the position of new facilities in the environment of the existing, to make the distance between the selected and the existing facilities as large as possible or as small as possible [1,2].The complexity of the location problem has led to the formulation of numerous mathematical models that are applied to describe the existing activities, as well as for the location of new facilities which need to efficiently perform certain services or activities
It is necessary to find the elementary path of maximum reliability to each of the six warehouses
The described problem can be observed as a subproblem of the problem of determining the location of k warehouse to maximize the system reliability
Summary
The complexity of the location problem has led to the formulation of numerous mathematical models that are applied to describe the existing activities, as well as for the location of new facilities which need to efficiently perform certain services or activities. An overview of location problems is given in [1,3]. As the basic network location models in [1], the following are listed; Set Covering Location Problem (SCLP), Maximal Covering Location. The robust optimization approach to the p-center location problem has been given in [4]. Adeleke and Olukanni described models which have been adapted to problems relating to waste management: Single Facility Location
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