On tie breaking in competitive location under binary customer behavior

• We develop a location model for an entering firm based on a new tie breaking rule in case of ties in customer maximum utility.
• The new tie breaking rule lead to better estimation of real market share captured by the entering firm.
• The proposed model let obtain better locations than other location models which use old tie breaking rules based on a fixed assignment of demand.
• An illustrative example is presented which show a comparison between the old and the new tie breaking rules.

Ties in customer facility choice may occur when the customer selects the facility with maximum utility to be served. In the location literature ties in maximum utility are broken by assigning a fixed proportion of the customer demand to the facilities with maximum utility which are owned by the entering firm. This tie breaking rule does not take into account the number of tied facilities of both the entering firm and its competitors. In this paper we introduce a more realistic tie breaking rule which assigns a variable proportion of customer demand to the entering firm depending on the number of tied facilities. We present a general framework in which optimal locations for the old and the new tie breaking rules can be obtained through Integer Linear Programming formulations of the corresponding location models. The optimal locations are obtained for the old tie breaking rule for different values of the fixed proportion and a comparison with the results obtained for the new tie breaking rule is drawn with data of Spanish municipalities in a variety of scenarios. Finally, some conclusions are presented.