On complexity of the bilevel location and pricing problems

We consider the bilevel mixed integer location and pricing problems. Each problem is determined by the optimization problems of the upper and lower levels of which the first describes the choice of location and pricing, while the second models the reaction of the customers on the upper-level solutio...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics Vol. 8; no. 4; pp. 574 - 581
Main Authors: Panin, A. A., Plyasunov, A. V.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.10.2014
Springer Nature B.V
Subjects:
Complexity
Customers
Integer programming
Manufacturers
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Mills
Mixed integer
Optimization
Prices
Pricing
Pricing policies
Strategy
Studies
Poly-APX-completeness
AP-reducibility
bilevel problem
computational complexity and approximation complexity
location
NP-hardness in the strong sense
pricing
ISSN:1990-4789, 1990-4797
Online Access:Get full text
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Summary:We consider the bilevel mixed integer location and pricing problems. Each problem is determined by the optimization problems of the upper and lower levels of which the first describes the choice of location and pricing, while the second models the reaction of the customers on the upper-level solution. The article focuses on studying the computational complexity of bilevel problems with various pricing strategies: uniform, mill, and discriminatory pricing. We show that, for an arbitrary pricing strategy, the corresponding optimization problem is NP-hard in the strong sense, belongs to the class Poly-APX, and is complete in it with respect to AP-reducibility.
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ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478914040152