IBM Research Report Minimum Up/Down Polytopes of the Unit Commitment Problem with Start-Up Costs
By D. Rajan, S. Takriti. 2005
270 citations recorded by the source corpus.
View Paper: https://www.semanticscholar.org/paper/b88642e36b414d5929fed48593d0ac46ae3e2070
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Citations in the corpus
- A Convex Primal Formulation for Convex Hull Pricing (2016, unknown): “Therefore, D2(1, 1) = D2(1, 0) = D2(0, 1) = D2(0, 0), so that we can only consider the case D2(1, 1), which is the case considered in the original proof of [30].”
- Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem (2012, methodology): “In [6], Rajan and Takriti claim that the constraints (14) and (15), along with the following logical constraints and variable-bound constraints, define the convex hull of all feasible solutions in the minimum up and downtime polytope:”
- A new MILP based approach for unit commitment in power production planning (2013, background): “In [22] the authors show that these inequalities are facets to the convex hull of the set CT(T,T) which is the projection of the problem in the space of variables y and x.”
- Conic relaxations of the unit commitment problem (2017, background): “[9] propose a set of valid inequalities (turn on/off) instead of the simple minimum upand down-time constraints to be able to solve hard cases of the UC problem by adopting a branch-and-cut technique.”
- A State Transition MIP Formulation for the Unit Commitment Problem (2018, background): “Following [11], the minimum uptime and downtime constraints are best formulated using the following constraints: ∑t i=t−U Tg +1 sg,i ≤ xg,t g ∈ G, t ∈ T , (7a) ∑t i=t−DTg +1 sg,i ≤ 1 − xg,t−DTg g ∈ G, t ∈ T .”
- An MILP Based Formulation for Short-Term Hydro Generation Scheduling With Analysis of the Linearization Effects on Solution Feasibility (2013, background): “Many useful skills are available to transform (14) into an MILP formulation (for example, the methods given in [38] and [40]).”
- Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem (2013, methodology): “These two formulations have been recognized as computationally efficient in the literature [9], [19], [21], [22], [28].”