A polyhedral study of production ramping

Pelin Damcı-Kurt, Simge Küçükyavuz*, Deepak Rajan, Alper Atamtürk

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


We give strong formulations of ramping constraints—used to model the maximum change in production level for a generator or machine from one time period to the next—and production limits. For the two-period case, we give a complete description of the convex hull of the feasible solutions. The two-period inequalities can be readily used to strengthen ramping formulations without the need for separation. For the general case, we define exponential classes of multi-period variable upper bound and multi-period ramping inequalities, and give conditions under which these inequalities define facets of ramping polyhedra. Finally, we present exact polynomial separation algorithms for the inequalities and report computational experiments on using them in a branch-and-cut algorithm to solve unit commitment problems in power generation.

Original languageEnglish (US)
Pages (from-to)175-205
Number of pages31
JournalMathematical Programming
Issue number1-2
StatePublished - Jul 1 2016


  • Co-generation
  • Computation
  • Convex hull
  • Facets
  • Polytope
  • Production smoothing
  • Ramping
  • Unit commitment
  • Valid inequalities

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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