Complexity of product positioning and ball intersection problems

Complexity of product positioning and ball intersection problems

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Article ID: iaor20041882
Country: United States
Volume: 20
Issue: 4
Start Page Number: 885
End Page Number: 894
Publication Date: Nov 1995
Journal: Mathematics of Operations Research
Authors: , ,
Keywords: marketing
Abstract:

The product positioning problem consists in choosing the attributes of a new product in such a way as to maximize its market share, i.e., to attract a maximum number of customers. Mathematically, the problem can be formulated as follows: given a set of balls (with respect to some norm) and a weight associated to each ball, find a point which maximizes the sum of the weights of the balls containing it. The complexity of this problem is investigated in the case of the L and of the Euclidean norms. In both cases, the problem is proved to be NP-hard, but to be polynomially solvable when the dimension of the space is fixed.

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