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Optimizing Paths with Random Parameter Distributions
Abstract
This research is grounded in the view that organizations are information processing systems. Organizations design their structure, processes, and information technologies for the purpose of processing, exchanging, and distributing the information required for their functions. The volume of information exchanged is not always the same. Thus in order to provide an efficient process of communication we propose an algorithm which determines the path that minimizes the expected value of an utility function over a dynamic probabilistic network with discrete or continuous real random variables (parameters) associated to each emerging arc. To obtain the optimal dynamic path from a source to sink node in the discrete case, we use a generalization of Bellman first-in-first-out labeling correcting algorithm used to determine the shortest path in directed networks with deterministic parameters associated to each arc. In the case where arc parameters are continuous random variables we propose algorithms involving multi-objective optimization. Additionally, some initialization techniques that improve the running times without jeopardizing memory are also considered. The topology of the networks is not known in advance, which means that we only have knowledge of the incoming (outgoing) arcs, and their parameters, of some specific node once we reach it. Thus the optimal path is determined in a dynamic way. We also present computational results for networks with 100 up to 10,000 nodes and densities 2, 5, and 10.
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