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Optimal flows in stochastic dynamic networks with congestion. (English) Zbl 0771.90044

Summary: This paper presents a method for finding optimal flows in a dynamic network with random inputs into the system and congestion limits on flow. This model has been used in deterministic settings to represent dynamic traffic assignment and job shop routing. This paper builds on the deterministic results to show that a globally optimal solution in the stochastic problem may be obtained by a sequence of linear optimizations. A decomposition algorithm for this procedure is presented that efficiently solves problems with large-scale deterministic equivalents of up to 66,000 variables.

MSC:

90B15 Stochastic network models in operations research
90B06 Transportation, logistics and supply chain management
90-08 Computational methods for problems pertaining to operations research and mathematical programming

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