Upper bounds for objective functions of discrete competitive facility location problems |
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Authors: | V L Beresnev |
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Institution: | (1) Department of Finance and Banking, Kun Shan University, Tainan Hsien, 71003, Taiwan, Republic of China;(2) Department of Applied Economics, National University of Kaohsiung, No.700, Kaohsiung University Road, Nan-Tzu District 811, Kaohsiung, Taiwan, Republic of China;; |
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Abstract: | Under study is the problem of locating facilities when two competing companies successively open their facilities. Each client
chooses an open facility according to his own preferences and return interests to the leader firm or to the follower firm.
The problem is to locate the leader firm so as to realize the maximum profit (gain) subject to the responses of the follower
company and the available preferences of clients. We give some formulations of the problems under consideration in the form
of two-level integer linear programming problems and, equivalently, as pseudo-Boolean two-level programming problems. We suggest
a method of constructing some upper bounds for the objective functions of the competitive facility location problems. Our
algorithm consists in constructing an auxiliary pseudo-Boolean function, which we call an estimation function, and finding the minimum value of this function. For the special case of the competitive facility location problems on paths,
we give polynomial-time algorithms for finding optimal solutions. Some results of computational experiments allow us to estimate
the accuracy of calculating the upper bounds for the competitive location problems on paths. |
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