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Aggregation without Loss of Optimality in Competitive Location Models

机译:竞争性位置模型中的聚合而不损失最优性

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摘要

In the context of competitive facility location problems demand points often have to be aggregated due to computational intractability. However, usually this spatial aggregation biases the value of the objective function and the optimality of the solution cannot be guaranteed for the original model. We present a preprocessing aggregation method to reduce the number of demand points which prevents this loss of information, and therefore avoids the possible loss of optimality. It is particularly effective in the frequent situation with a large number of demand points and a comparatively low number of potential facility sites, and coverage denned by spatial nearness. It is applicable to any spatial consumer behaviour model of covering type. This aggregation approach is applied in particular to a Competitive Maximal Covering Location Problem and to a recently developed von Stackelberg model. Some empirical results are presented, showing that the approach may be quite effective.
机译:在竞争性设施选址问题的背景下,由于计算上的难点性,经常必须汇总需求点。但是,通常这种空间聚集会使目标函数的值产生偏差,并且原始模型无法保证解的最优性。我们提出了一种预处理聚合方法来减少需求点的数量,这可以防止这种信息丢失,从而避免了可能的最优性损失。在需求量大,潜在设施站点数量相对较少且覆盖范围受空间邻近性限制的频繁情况下,此功能特别有效。它适用于任何覆盖类型的空间消费者行为模型。这种聚合方法尤其适用于竞争性最大覆盖位置问题和最近开发的冯·斯塔克伯格模型。提出了一些经验结果,表明该方法可能非常有效。

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