The min-up/min-down unit commitment polytope

Pascale Bendotti (), Pierre Fouilhoux () and Cécile Rottner ()
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Pascale Bendotti: Sorbonne Universités, Université Pierre et Marie Curie
Pierre Fouilhoux: Sorbonne Universités, Université Pierre et Marie Curie
Cécile Rottner: Sorbonne Universités, Université Pierre et Marie Curie

Journal of Combinatorial Optimization, 2018, vol. 36, issue 3, No 17, 1024-1058

Abstract: 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 forecast 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 (Minimum up/down polytopes of the unit commitment problem with start-up costs. IBM Research Report, 2005). 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 and Cut algorithm, using up-set and interval up-set inequalities.

Keywords: Unit commitment problem (UCP); Min-up/min-down; Polytope; Facet; Branch and Cut (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-018-0273-y

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