TY - JOUR

T1 - An upper bound for the competitive location and capacity choice problem with multiple demand scenarios

AU - Beresnev, V. L.

AU - Melnikov, A. A.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - A new mathematical model is considered related to competitive location problems where two competing parties, the Leader and the Follower, successively open their facilities and try to win customers. In the model, we consider a situation of several alternative demand scenarios which differ by the composition of customers and their preferences.We assume that the costs of opening a facility depend on its capacity; therefore, the Leader, making decisions on the placement of facilities, must determine their capacities taking into account all possible demand scenarios and the response of the Follower. For the bilevel model suggested, a problem of finding an optimistic optimal solution is formulated. We show that this problem can be represented as a problem of maximizing a pseudo- Boolean function with the number of variables equal to the number of possible locations of the Leader’s facilities.We propose a novel systemof estimating the subsets that allows us to supplement the estimating problems, used to calculate the upper bounds for the constructed pseudo-Boolean function, with additional constraints which improve the upper bounds.

AB - A new mathematical model is considered related to competitive location problems where two competing parties, the Leader and the Follower, successively open their facilities and try to win customers. In the model, we consider a situation of several alternative demand scenarios which differ by the composition of customers and their preferences.We assume that the costs of opening a facility depend on its capacity; therefore, the Leader, making decisions on the placement of facilities, must determine their capacities taking into account all possible demand scenarios and the response of the Follower. For the bilevel model suggested, a problem of finding an optimistic optimal solution is formulated. We show that this problem can be represented as a problem of maximizing a pseudo- Boolean function with the number of variables equal to the number of possible locations of the Leader’s facilities.We propose a novel systemof estimating the subsets that allows us to supplement the estimating problems, used to calculate the upper bounds for the constructed pseudo-Boolean function, with additional constraints which improve the upper bounds.

KW - bilevel programming

KW - competitive facility location

KW - upper bound

UR - http://www.scopus.com/inward/record.url?scp=85036458617&partnerID=8YFLogxK

U2 - 10.1134/S1990478917040020

DO - 10.1134/S1990478917040020

M3 - Article

AN - SCOPUS:85036458617

VL - 11

SP - 472

EP - 480

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -