1 February 2020

1 March 2020

19 May 2020

#### Abstract

*a new facility will be opened only if a minimal market share is captured in the short-term*. To check that, it is necessary to know the exact captured demand by each new facility. It is supposed that customers follow the partially binary choice rule to satisfy its demand. If there are several new facilities with maximal attraction for a customer, we consider that the proportion of demand captured by the entering firm will be equally distributed among such facilities (equity-based rule). This ties breaking rule involves that we will deal with a nonlinear constrained discrete competitive facility location problem. Moreover, minimal attraction conditions for customers and distances approximated by intervals have been incorporated to deal with a more realistic model. To solve this nonlinear model, we first linearize the model, which allows to solve small size problems because of its complexity, and then, for bigger size problems, a heuristic algorithm is proposed, which could also be used to solve other constrained problems.

#### Biographies

**P. Fernández** is currently teaching statistics and operational research at the University of Murcia. He received his PhD in mathematics from the University of Murcia. His research interests include graph theory, network optimization, discrete multi-objective optimization, and locational analysis, actually on discrete competitive facility location models. He is a member of the Spanish Society of Statistical and Operational Research and a member of the EURO Working Group on Locational Analysis (EWGLA).

**A. Lančinskas** received the doctoral degree in informatics from Institute of Mathematics and Informatics of Vilnius University, in 2013. Currently he works as a researcher and lecturer at Vilnius University. His research interest is focused on development and investigation of global and multi-objective optimization algorithms, and their parallelization.

**B. Pelegrín** is a professor of statistics and operations research and head of the Research Group on Operations Research at the University of Murcia (Spain). His main research areas are locational analysis, game theory, and network optimization. He has published more than 60 papers in recognized journals and has been an associated/invited editor of *Studies on Locational Analysis*, *TOP*, and *Computers and Operations Research*.

**J. Žilinskas** is a principal researcher and the head of Recognition Processes Department at Vilnius University Institute of Mathematics and Informatics, Lithuania. His research interests include global optimization, parallel computing, data analysis and visualization. He is a member of editorial boards of *Central European Journal of Computer Science*, *Central European Journal of Engineering*, *Informatica*, *Journal of Global Optimization*, *Mathematical Modelling and Analysis*, and *Optimization Letters*.