On the Sum-Product Ratio Problem and its Applications
Operations Research Letters (Forthcoming)
13 Pages Posted: 6 Apr 2016 Last revised: 25 May 2016
Date Written: September 5, 2015
We study the so-called sum-product ratio problem, under which the numerate is the sum of numbers in a subset and the denominator is the product of numbers in the same subset. Unlike the sum-sum ratio problem, which corresponds to the assortment problem under the multinomial logit model, the sum-product ratio problem is generally NP-complete. We develop a fully polynomial-time approximation scheme and discuss several potential applications and useful extensions.
Keywords: Sum-Product Ratio, NP-Hardness, Fully Polynomial-Time Approximation Scheme, Consideration Set
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