TY - JOUR

T1 - A capacitated competitive facility location problem

AU - Beresnev, V. L.

AU - Melnikov, A. A.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - We consider a mathematical model similar in a sense to competitive location problems. There are two competing parties that sequentially open their facilities aiming to “capture” customers and maximize profit. In our model, we assume that facilities’ capacities are bounded. The model is formulated as a bilevel integer mathematical program, and we study the problem of obtaining its optimal (cooperative) solution. It is shown that the problem can be reformulated as that of maximization of a pseudo-Boolean function with the number of arguments equal to the number of places available for facility opening. We propose an algorithm for calculating an upper bound for values that the function takes on subsets which are specified by partial (0, 1)-vectors.

AB - We consider a mathematical model similar in a sense to competitive location problems. There are two competing parties that sequentially open their facilities aiming to “capture” customers and maximize profit. In our model, we assume that facilities’ capacities are bounded. The model is formulated as a bilevel integer mathematical program, and we study the problem of obtaining its optimal (cooperative) solution. It is shown that the problem can be reformulated as that of maximization of a pseudo-Boolean function with the number of arguments equal to the number of places available for facility opening. We propose an algorithm for calculating an upper bound for values that the function takes on subsets which are specified by partial (0, 1)-vectors.

KW - bilevel programming

KW - competitive facility location

KW - upper bound

UR - http://www.scopus.com/inward/record.url?scp=84961674893&partnerID=8YFLogxK

U2 - 10.1134/S1990478916010075

DO - 10.1134/S1990478916010075

M3 - Article

AN - SCOPUS:84961674893

VL - 10

SP - 61

EP - 68

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -