Optimal algorithms for some inverse uncapacitated facility location problems on networks

Abstract

This paper is concerned with two variants of the inverse uncapacitated facility location problem with service cost modifications on tree networks under the rectilinear norm. In the first variant, the aim is to modify the underlying service costs in the cheapest possible way with respect to modification bounds such that a set of predetermined facility locations becomes optimal under the new parameters. Two types of this problem are investigated. The second variant asks to modify the service costs within an associated budget until the predetermined facility locations become as close as possible to the customers. Two types of this problem are also studied. We develop exact optimal algorithms for solving the problems under investigation. By an example, the efficiency of the proposed algorithms is illustrated.

Keywords:

• Uncapacitated facility location
• inverse optimization
• tree networks

AMS Subject Classifications:

• 90B80
• 90B85
• 90C27
• 90C35

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Mehran Hasanzadeh

Mehran Hasanzadeh is a PhD candidate within the Department of Applied Mathematics at the Sahand University of Technology, Tabriz, Iran. He received his BSc degree from the University of Mohaghegh Ardabili, Ardabil, Iran, in 2011, and MSc degree from University of Tabriz, Tabriz, Iran, in 2015. His research interests are mainly in the area of combinatorial optimization, facility location and inverse optimization.

Behrooz Alizadeh

Dr. Behrooz Alizadeh finished his MSc study at the Tarbiat Modares University, Tehran, Iran, in 2001. He received his PhD in Applied Mathematics (Operations Research) from Graz University of Technology, Graz, Austria, in 2009. Dr. Alizadeh is currently an Associate Professor of Operations Research & Optimization at the Department of Applied Mathematics, Sahand University of Technology, Tabriz, Iran. The main research interests of Dr. Alizadeh include facility location theory, network optimization, combinatorial optimization, inverse optimization and engineering optimization. He has published more than 52 research papers in the scientific journals. He also serves as a member of board of directors in the Iranian Operations Research Society since 2013.

Fahimeh Baroughi

Dr. Fahimeh Baroughi received her PhD in Applied Mathematics (Operations Research) from the Graz University of Technology, Graz, Austria, in 2010. She works mainly in the area of combinatorial optimization, location theory, uncertain programming and reverse optimization. Dr. Baroughi is currently an Associate Professor at the Department of Applied Mathematics, Sahand University of Technology, Tabriz, Iran.