The Summed Start-up Costs in a Unit Commitment Problem

TL;DR

This paper establishes a novel connection between the facets of the start-up cost epigraph in unit commitment problems and binary trees, leading to improved linear representations and reduced integrality gaps.

Contribution

It introduces a bijective correspondence between epigraph facets and binary trees for concave start-up costs, along with an exponential H-representation and a linear separation algorithm.

Findings

Exponential H-representation of the start-up cost epigraph

Exact linear separation algorithm for the epigraph

Reduced integrality gap in unit commitment formulations

Abstract

We consider the sum of the incurred start-up costs of a single unit in a Unit Commitment problem. Our major result is a correspondence between the facets of its epigraph and some binary trees for concave start-up cost functions CU, which is bijective if CU is strictly concave. We derive an exponential H-representation of this epigraph, and provide an exact linear separation algorithm. These results significantly reduce the integrality gap of the Mixed Integer formulation of a Unit Commitment Problem compared to current literature.