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Exact approaches for competitive facility location with discrete attractiveness

March 2021
Optimization Letters 15(9)

March 2021
15(9)

Authors:

A*STAR

We study a variant of the competitive facility location problem, in which a company is to locate new facilities in a market where competitor’s facilities already exist. We consider the scenario where only a limited number of possible attractiveness levels is available, and the company has to select exactly one level for each open facility. The goal is to decide the facilities’ locations and attractiveness levels that maximize the profit. We apply the gravity-based rule to model the behavior of the customers and formulate a multi-ratio linear fractional 0–1 program. Our main contributions are the exact solution approaches for the problem. These approaches allow for easy implementations without the need for designing complicated algorithms and are “friendly” to the users without a solid mathematical background. We conduct computational experiments on the randomly generated datasets to assess their computational performance. The results suggest that the mixed-integer quadratic conic approach outperforms the others in terms of computational time. Besides that, it is also the most straightforward one that only requires the users to be familiar with the general form of a conic quadratic inequality. Therefore, we recommend it as the primary choice for such a problem.

Profit (φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}) and the number of new facilities (F) under different parameter values

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Optimization Letters (2021) 15:377–389

https://doi.org/10.1007/s11590-020-01596-x

ORIGINAL PAPER

Exact approaches for competitive facility location with

discrete attractiveness

Yun Hui Lin1·Qingyun Tian2

Received: 5 November 2019 / Accepted: 13 May 2020 / Published online: 19 May 2020

Abstract

We study a variant of the competitive facility location problem, in which a company

is to locate new facilities in a market where competitor’s facilities already exist. We

consider the scenario where only a limited number of possible attractiveness levels is

available, and the company has to select exactly one level for each open facility. The

goal is to decide the facilities’ locations and attractiveness levels that maximize the

proﬁt. We apply the gravity-based rule to model the behavior of the customers and

formulate a multi-ratio linear fractional 0–1 program. Our main contributions are the

exact solution approaches for the problem. These approaches allow for easy implemen-

tations without the need for designing complicated algorithms and are “friendly” to

the users without a solid mathematical background. We conduct computational exper-

iments on the randomly generated datasets to assess their computational performance.

The results suggest that the mixed-integer quadratic conic approach outperforms the

others in terms of computational time. Besides that, it is also the most straightforward

one that only requires the users to be familiar with the general form of a conic quadratic

inequality. Therefore, we recommend it as the primary choice for such a problem.

Keywords Competitive facility location ·Gravity model ·Conic programming ·

Outer approximation ·Mixed-integer linear programming

1 Introduction

The classical competitive facility location problem (CFL) studies a “newcomer” com-

pany who enters a market where competitor’s facilities already exist. The company

BYun Hui Lin

linyunhui@u.nus.edu

1Department of Industrial Systems Engineering and Management, National University of

Singapore, Singapore, Singapore

2School of Civil and Environmental Engineering, Nanyang Technological University, Singapore,

Singapore

123

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Exact approaches for competitive facility location with discrete attractiveness

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