In the leader-follower, (r|p)-centroid or Stackelberg location problem, two players sequentially enter the market and compete to provide goods or services. This paper considers this competitive facility location problem in a discrete space. To solve it, the linear programming formulations for the leader and the follower are integrated into an algorithm which, in an iterative process, finds a solution by solving a sequence of these linear problems. We propose a matheuristic procedure that provides solutions for the leader via a kernel search algorithm. Taking into account binary and S-shaped customer choice rules, we present the computational results obtained and compare the exact algorithm with two versions of the kernel search procedure.

中文翻译：

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核搜索数学方法来解决离散的领导者-跟随者位置问题

在跟随者，（r | p）质心或Stackelberg位置问题中，两个参与者依次进入市场并竞争提供商品或服务。本文考虑了离散空间中的竞争性设施选址问题。为了解决该问题，将领导者和跟随者的线性规划公式集成到一个算法中，该算法在迭代过程中通过解决一系列这些线性问题来找到解决方案。我们提出了一种数学过程，该过程通过内核搜索算法为领导者提供解决方案。考虑到二进制和S形客户选择规则，我们介绍了获得的计算结果，并将精确算法与内核搜索程序的两个版本进行了比较。