Optimal Sizes of Facilities on a Linear Market

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Let n facilities be located on a bounded linear market and assume that demand for a homogenous commodity is uniformly distributed along that market. Initially each facility has a given size which determines its attraction to the customers. Independently at each facility a profit function is maximized by selecting new facility sizes. The individual optima are then combined and the optimization procedure is repeated. In a series of tests it is hown that such a decentralized optimization procedure quickly converges to an overall equilibrium.

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