The probabilistic customer’s choice rule with a threshold attraction value: Effect on the location of competitive facilities in the plane

• Published in: Computers & operations research Vol. 101; pp. 234 - 249
• Main Authors: Fernández, José, G.- Tóth, Boglárka, L. Redondo, Juana, M. Ortigosa, Pilar
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.01.2019; Pergamon Press Inc
• Subjects: Aircraft; Attraction; Competition; Computational study; Continuous location; Customer choice rule; Customers; Decision making; Evolutionary algorithm; Facilities; Interval branch-and-bound method; Operations research; Patronizing behavior; Probability; Competition; Patronizing behavior; Continuous location; Computational study; Evolutionary algorithm; Customer choice rule; Interval branch-and-bound method
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2018.08.001

•Choosing the correct choice rule in competitive location problems is extremely important.•Profit can decrease from the expected one if an unsuitable choice rule is considered.•The partially probabilistic choice rule is in many cases a more realistic assumption.•A facility is only patronized by demand points provided it has a minimum attraction level.•Ad hoc deterministic and metaheuristic algorithms are proposed to solve this discontinuous problem. The classical probabilistic choice rule assumes that customers patronize all the existing facilities. As this assumption may not be appropriate in some cases, in this paper a variant is investigated, in which a customer only patronizes those facilities for which he/she feels an attraction greater than or equal to a threshold value. Implicitly, this implies that there may be some unmet demand. We apply this modified rule to the problem of locating a single new facility in the plane. A comparison of the location decisions derived from the modified rule with those obtained with the classical proportional choice rule when solving the location model reveals that the profit that the locating chain may lose if an inadequate choice rule is employed may be quite high in some instances.