On tie breaking in competitive location under binary customer behavior

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.