This paper presents three reformulations for the well-known maximum capture location problem under multinomial logit choice. The problem can be cast as an integer fractional program and it has been the subject of several linear reformulations in the past. Here we develop two linear and a conic reformulation based on alternative treatments of fractional programs. Numerical experiments conducted on established sets of instances have shown that conic reformulation has greatly improved the solution times as well as the size of the solvable problems as compared to the most successful reformulations to date.

中文翻译：

---

多项式对数选择下最大捕获位置问题的线性和圆锥形式

本文针对多项式logit选择下的众所周知的最大捕获位置问题，提出了三种格式。可以将问题转换为整数小数程序，并且在过去，它已成为若干线性公式的主题。在这里，我们基于分数程序的替代处理，开发了两个线性和一个圆锥形的公式。在已建立的实例集上进行的数值实验表明，与迄今为止最成功的重构方法相比，圆锥形重构方法极大地缩短了求解时间，并缩短了可解决问题的大小。