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arXiv · 2203.00735

Permutatorial Optimization via the Permutahedron

J. Carlos Martinez Mori·Samitha Samaranayake
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Abstract

A water company decides to expand its network with a set of water lines, but it cannot build them all at once. However, it starts reaping benefits from a partial expansion. In what order should the company build the lines? We formalize a class of permutatorial problems with combinatorial/continuous subproblems capturing applications of incremental deployment. We show that, for additive/linear objective functions, efficient polyhedral methods for the subproblems extend to the permutatorial problem. Our main technical ingredient is the permutahedron.

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J. Carlos Martinez Mori, Samitha Samaranayake. 2022-07-26. Permutatorial Optimization via the Permutahedron. https://doi.org/10.1016/j.orl.2022.06.008

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