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The Min-up/Min-down Unit Commitment polytope

Pascale Bendotti (pascale.bendotti***at***edf.fr)
Pierre Fouilhoux (pierre.fouilhoux***at***lip6.fr)
CÚcile Rottner (cecile.rottner***at***edf.fr)

Abstract: The Min-up/min-down Unit Commitment Problem (MUCP) is to find a minimum-cost production plan on a discrete time horizon for a set of fossil-fuel units for electricity production. At each time period, the total production has to meet a forecasted demand. Each unit must satisfy minimum up-time and down-time constraints besides featuring production and start-up costs. A full polyhedral characterization of the MUCP with only one production unit is provided by Rajan and Takriti. In this article, we analyze polyhedral aspects of the MUCP with n production units. We first translate the classical extended cover inequalities of the knapsack polytope to obtain the so-called up-set inequalities for the MUCP polytope. We introduce the interval up-set inequalities as a new class of valid inequalities, which generalizes both up-set inequalities and minimum up-time inequalities. We provide a characterization of the cases when interval up-set inequalities are valid and not dominated by other inequalities. We devise an efficient Branch & Cut algorithm, using up-set and interval up-set inequalities.

Keywords: Unit Commitment Problem (UCP); Min-up/min-down; Polytope; Facet; Branch & Cut

Category 1: Combinatorial Optimization (Polyhedra )

Category 2: Combinatorial Optimization (Branch and Cut Algorithms )

Category 3: Applications -- OR and Management Sciences

Citation: Sorbonne UniversitÚs, UniversitÚ Pierre et Marie Curie, LIP6 CNRS UMR 7606, 4 Place Jussieu, 75005 Paris; EDF R&D, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France November, 2016

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Entry Submitted: 11/29/2016
Entry Accepted: 12/01/2016
Entry Last Modified: 06/21/2017

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