A Discrete Competitive Facility Location Model with Minimal Market Share Constraints and Equity-Based Ties Breaking Rule

Fernández, Pascual; Lančinskas, Algirdas; Pelegrín, Blas; Žilinskas, Julius

doi:10.15388/20-INFOR410

Informatica

A Discrete Competitive Facility Location Model with Minimal Market Share Constraints and Equity-Based Ties Breaking Rule

Volume 31, Issue 2 (2020), pp. 205–224

Pascual Fernández Algirdas Lančinskas Blas Pelegrín Julius Žilinskas

https://doi.org/10.15388/20-INFOR410

Pub. online: 19 May 2020 Type: Research Article

Open Access

Received
1 February 2020

Accepted
1 March 2020

Published
19 May 2020

Abstract

We consider a geographical region with spatially separated customers, whose demand is currently served by some pre-existing facilities owned by different firms. An entering firm wants to compete for this market locating some new facilities. Trying to guarantee a future satisfactory captured demand for each new facility, the firm imposes a constraint over its possible locations (a finite set of candidates): 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.

References

Al-Yakoob, S.M., Sherali, H.D. (2018). A mathematical modelling and optimization approach for a maritime facility location transshipment problem. Informatica, 29, 609–632.

Balakrishnan, P., Storbeck, J. (1991). McTRESH: modeling maximum coverage with threshold constraint. Environment and Planning B, 18, 459–472.

Benati, S., Hansen, P. (2002). The maximum capture problem with random utilities: problem formulation and algorithms. European Journal of Operational Research, 143, 518–530.

Biesinger, B., Hu, B., Raidl, G. (2016). Models and algorithms for competitive facility location problems with different customer behaviour. Annals of Mathematics and Artificial Intelligence, 76(1), 93–119.

Colomé, R., Lourenço, H.R., Serra, D. (2003). A new chance-constrained maximum capture location problem. Annals of Operations Research, 122, 121–139.

Drezner, T. (1995). Competitive facility location in the plane. In: Drezner, Z. (Ed.), Facility Location: A Survey of Applications and Methods, pp. 285–300.

Drezner, T., Drezner, Z. (2004). Finding the optimal solution to the Huff based competitive location model. Computational Management Science, 1(2), 193–208.

Drezner, T., Drezner, Z., Shiode, S. (2002). A threshold satisfying competitive location model. Journal of Regional Science, 42(2), 287–299.

Eiselt, H., Laporte, G., Thisse, J.F. (1993). Competitive location models: a framework and bibliography. Transportation Science, 27, 44–54.

Eiselt, H., Marianov, V., Drezner, T. (2015). Competitive location models. In: Laporte, G., Nickel, S., da Gama, F.S. (Eds.), Location Science, pp. 365–398.

Fernández, P., Pelegrín, B., Lančinskas, A., Žilinskas, J. (2017). New heuristic algorithms for discrete competitive location problems with binary and partially binary customer behavior. Computers and Operations Research, 79, 12–18.

FICO Xpress Mosel (2014). Fair Isaac Corporation.

Francis, R.L., Lowe, T.J., Tamir, A. (2002). Demand point aggregation for location models. In: Drezner, Z., Hamacher, H. (Eds.), Facility Location: Application and Theory, pp. 207–232.

Friesz, T.L., Miller, T.C., Tobin, R.L. (1988). Competitive network facility location models: a survey. Papers of the Regional Science Association, 65, 47–57.

Haase, K., Muller, S. (2014). A comparison of linear reformulations for multinomial logit choice probabilities in facility location models. European Journal of Operational Research, 232, 689–691.

Hakimi, S.L. (1990). Location with spatial interactions, competitive locations. In: Mirchandani, P.B., Francis, R.L. (Eds.), Discrete Location Theory, pp. 439–478.

Hodgson, M.J. (1978). A location-allocation model maximizing consumers’ welfare. Regional Studies, 15, 493–506.

Hotelling, H. (1929). Stability in competition. Economic Journal, 39, 41–57.

Huff, D.L. (1964). Defining and estimating a trading area. Journal of Marketing, 28, 34–38.

Kochetov, Y., Kochetova, N., Plyasunov, A. (2013). A matheuristic for the leader-follower facility location and design problem. In: Lau, H., Van Hentenryck, P., Raidl, G. (Eds.), Proceedings of the 10th Metaheuristics International Conference (MIC 2013), pp. 32/1–32/3.

Ljubić, I., Moreno, E. (2018). Outer approximation and submodular cuts for maximum capture facility location problems with random utilities. European Journal of Operational Research, 266, 46–56.

McGarvey, R.G., Cavalier, T.M. (2005). Constrained location of competitive facilities in the plane. Computers and Operations Research, 32, 359–378.

Pelegrín, B., Fernández, P., García, M.D. (2015). On tie breaking in competitive location under binary customer behavior. OMEGA-International Journal of Management Science, 52, 156–167.

Plastria, F. (2001). Static competitive facility location: an overview of optimisation approaches. European Journal of Operational Research, 129, 461–470.

Plastria, F., Vanhaverbeke, L. (2008). Discrete models for competitive location with foresight. Computers and Operations Research, 35, 683–700.

Revelle, C.S., Eiselt, H.A. (2005). Location analysis: a synthesis and a survey. European Journal of Operational Research, 165, 1–19.

Serra, D., ReVelle, C., Rosing, K. (1999a). Surviving in a competitive spatial market: the threshold capture model. Journal of Regional Science, 39(4), 637–652.

Serra, D., Eiselt, H.A., Laporte, G., ReVelle, C.S. (1999b). Market capture models under various customer-choice rules. Environment and Planning B: Planning and Design, 26, 741–750.

Suárez-Vega, R., Santos-Peñate, D., Dorta-González, P. (2004). Competitive multifacility location on networks: the $(r/{X_{p}})$-medianoid problem. Journal of Regional Science, 44, 569–588.

Wilson, A.G. (1976). Retailers’ profits and consumers’ welfare in a spacial interaction shopping model. In: Masser, I. (Ed.), Theory and Practice in Regional Science, pp. 42–59.

Biographies

Fernández Pascual

pfdez@um.es

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).

Lančinskas Algirdas

algirdas.lancinskas@mif.vu.lt

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.

Pelegrín Blas

pelegrin@um.es

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.

Žilinskas Julius

julius.zilinskas@mif.vu.lt

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.

Full article Related articles Cited by

Open access article under the CC BY license.

Keywords

location competitive model heuristic algorithms

Funding

This research has been supported by the Fundación Séneca (The Agency of Science and Technology of the Region of Murcia) under the research project 20817/PI/18, and by a Grant (No. S-MIP-17-67) from the Research Council of Lithuania.

Metrics

since January 2020

1831 Article info views	713 Full article views
767 PDF downloads	272 XML downloads

RSS

Authors

Abstract

References

Biographies

Export citation

Copy and paste formatted citation

Download citation in file