Abstract The p-median problem is one of the true classic problems of location science and has been applied in many ways. It involves the location of p-facilities on a network where the objective is to minimize the weighted distance of serving all demand. This problem was originally proposed by Hakimi (1964, 1965) where the facilities were telephone switching centers and the connections represent wire stretched between each customer and their closest facility. It has since been viewed as the quintessential public facility location problem as it involves placing facilities as close to as possible on the average to each demand. This problem was originally formulated as an integer-programming problem by ReVelle and Swain (1970). Their formulation has withstood the test of time as most of the approaches to optimally solve the p-median problem involve a form of this model. There are several notable exceptions to the use of the classical formulation which take advantage of the underlying distance matrix defined by regular networks (Elloumi 2010; Garcia et al., 2011), such as grid-defined networks. We demonstrate that inherent properties of the distance matrix defined for regular networks can be taken into account, resulting in a reduced, frugal form of the classic p-median model of ReVelle and Swain (1970). This new model called CARS is tested and compared to a form of the original model, recent computational experience presented by Daskin and Maass (2015) and to a form of the model used by Garcia et al. (2011). This test demonstrates that this new, simple model is very competitive to other approaches in solving sizable p-median problems using off-the-shelf commercial software.

中文翻译：

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解决规则和格子网络上的 p 中值问题

摘要 p 中值问题是定位科学中真正的经典问题之一，并已在许多方面得到应用。它涉及网络上 p 设施的位置，其目标是最小化满足所有需求的加权距离。这个问题最初是由 Hakimi (1964, 1965) 提出的，其中设施是电话交换中心，连接代表每个客户和他们最近的设施之间延伸的电线。从那时起，它就被视为典型的公共设施选址问题，因为它涉及将设施放置在尽可能靠近每个需求的平均位置。这个问题最初由 ReVelle 和 Swain (1970) 制定为整数规划问题。他们的公式经受住了时间的考验，因为大多数优化解决 p 中值问题的方法都涉及这种模型的一种形式。使用经典公式有几个值得注意的例外，这些公式利用了常规网络（Elloumi 2010；Garcia 等，2011）定义的基础距离矩阵，例如网格定义的网络。我们证明可以考虑为常规网络定义的距离矩阵的固有属性，从而产生 ReVelle 和 Swain（1970）的经典 p 中值模型的简化、节俭形式。这个名为 CARS 的新模型经过测试，并与原始模型的一种形式、Daskin 和 Maass（2015 年）提出的最新计算经验以及 Garcia 等人使用的模型形式进行了比较。(2011)。该测试表明，这种新的、