On the Sum-Product Ratio Problem and its Applications

Operations Research Letters (Forthcoming)

13 Pages Posted: 6 Apr 2016 Last revised: 25 May 2016

See all articles by Ruxian Wang

Ruxian Wang

Johns Hopkins University - Carey Business School

Date Written: September 5, 2015

Abstract

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

Suggested Citation

Wang, Ruxian, On the Sum-Product Ratio Problem and its Applications (September 5, 2015). Operations Research Letters (Forthcoming). Available at SSRN: https://ssrn.com/abstract=2758201 or http://dx.doi.org/10.2139/ssrn.2758201

Ruxian Wang (Contact Author)

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

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