Browsing by Subject "Triangle inequality"

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    A bilevel uncapacitated location/pricing problem with Hotelling access costs in one-dimensional space
    (International Conference on Information Systems, Logistics and Supply Chain, 2016) Arbib, C.; Pınar, Mustafa Ç.; Tonelli, M.
    We formulate a spatial pricing problem as bilevel non-capacitated location: a leader first decides which facilities to open and sets service prices taking competing offers into account; then, customers make individual decisions minimizing individual costs that include access charges in the spirit of Hotelling. Both leader and customers are assumed to be risk-neutral. For non-metric costs (i.e., when access costs do not satisfy the triangle inequality), the problem is NP-hard even if facilities can be opened at no fixed cost. We describe an algorithm for solving the Euclidean 1-dimensional case (i.e., with access cost defined by the Euclidean norm on a line) with fixed opening costs and a single competing facility.