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On the Logit Approach to Competitive Facility Location
Author(s) -
Drezner Zvi,
Wesolowsky George O.,
Drezner Tammy
Publication year - 1998
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/1467-9787.00094
Subject(s) - logit , facility location problem , mixed logit , logistic regression , function (biology) , logistic function , mathematical optimization , computer science , point (geometry) , econometrics , mathematics , statistics , geometry , evolutionary biology , biology
The random utility model in competitive facility location is one approach for estimating the market share captured by a retail facility in a competitive environment. However, it requires extensive computational effort for finding the optimal location for a new facility because its objective function is based on a k ‐dimensional integral. In this paper we show that the random utility model can be approximated by a logit model. The proportion of the buying power at a demand point that is attracted to the new facility can be approximated by a logit function of the distance to it. This approximation demonstrates that using the logit function of the distance for estimating the market share is theoretically founded in the random utility model. A simplified random utility model is defined and approximated by a logit function. An iterative Weiszfeld‐type algorithm is designed to find the best location for a new facility using the logit model. Computational experiments show that the logit approximation yields a good location solution to the random utility model.