A polyhedral study of production ramping

Damci-Kurt, Pelin; Kucukyavuz, Simge; Rajan, Deepak; Atamturk, Alper

doi:10.1007/s10107-015-0919-9

Title: A polyhedral study of production ramping

Abstract

Here, 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.

Authors:

Damci-Kurt, Pelin ^[1]; Kucukyavuz, Simge ^[1]; Rajan, Deepak ^[2]; Atamturk, Alper ^[3]

The Ohio State Univ., Columbus, OH (United States). Dept. of Integrated Systems Engineering
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
Univ. of California, Berkeley, CA (United States). Dept. of Industrial Engineering and Operations Research

Publication Date:: Fri Jun 12 00:00:00 EDT 2015

Research Org.:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1455405

Report Number(s):: LLNL-JRNL-732987
Journal ID: ISSN 0025-5610; 884544

Grant/Contract Number:: AC52-07NA27344; 0970180

Resource Type:: Accepted Manuscript

Journal Name:: Mathematical Programming

Additional Journal Information:: Journal Volume: 158; Journal Issue: 1-2; Journal ID: ISSN 0025-5610

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; Ramping; unit commitment; co-generation; production smoothing, convex hull; polytope; valid inequalities; facets; computation

Citation Formats


                    Damci-Kurt, Pelin, Kucukyavuz, Simge, Rajan, Deepak, and Atamturk, Alper. A polyhedral study of production ramping.  United States: N. p., 2015. 
Web.  doi:10.1007/s10107-015-0919-9.

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                    Damci-Kurt, Pelin, Kucukyavuz, Simge, Rajan, Deepak, & Atamturk, Alper. A polyhedral study of production ramping.  United States.  https://doi.org/10.1007/s10107-015-0919-9

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                    Damci-Kurt, Pelin, Kucukyavuz, Simge, Rajan, Deepak, and Atamturk, Alper. Fri .  
"A polyhedral study of production ramping".  United States.  https://doi.org/10.1007/s10107-015-0919-9.  https://www.osti.gov/servlets/purl/1455405.

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@article{osti_1455405,

  title        = {A polyhedral study of production ramping},

  author       = {Damci-Kurt, Pelin and Kucukyavuz, Simge and Rajan, Deepak and Atamturk, Alper},

  abstractNote = {Here, 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.},

  doi          = {10.1007/s10107-015-0919-9},

  journal      = {Mathematical Programming},

  number       = 1-2,

  volume       = 158,

  place        = {United States},

  year         = {Fri Jun 12 00:00:00 EDT 2015},

  month        = {Fri Jun 12 00:00:00 EDT 2015}

}

Copy to clipboard

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Works referencing / citing this record:

Tight MIP formulations for bounded up/down times and interval-dependent start-ups
journal, October 2016

Queyranne, Maurice; Wolsey, Laurence A.
Mathematical Programming, Vol. 164, Issue 1-2
DOI: 10.1007/s10107-016-1079-2

Lifted polymatroid inequalities for mean-risk optimization with indicator variables
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Atamtürk, Alper; Jeon, Hyemin
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Parallel matheuristics for the discrete unit commitment problem with min-stop ramping constraints
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Dupin, Nicolas; Talbi, El-ghazali
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Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables
preprint, January 2017

Atamturk, Alper; Jeon, Hyemin
arXiv
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Similar Records

Title: A polyhedral study of production ramping

Abstract

Citation Formats

Solving unit commitment problems with general ramp constraints journal, June 2008

Tighter Approximated MILP Formulations for Unit Commitment Problems journal, February 2009

Unit commitment literature synopsis journal, January 1994

Generating Unit Commitment by Dynamic Programming journal, May 1966

A strong conic quadratic reformulation for machine-job assignment with controllable processing times journal, May 2009

Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem journal, November 2013

Decomposition approach to problem of unit commitment schedule for hydrothermal systems journal, January 1980

Production Smoothing with Fluctuating Price journal, January 1975

A Tutorial on Production Smoothing and Work Force Balancing journal, December 1967

Optimal planning of cogeneration production with provision of ancillary services journal, February 2013

A Branch-and-Bound Algorithm for Unit Commitment journal, February 1983

Unit commitment by tabu search journal, January 1998

An effective heuristic for combined heat-and-power production planning with power ramp constraints journal, March 2007

A Computationally Efficient Mixed-Integer Linear Formulation for the Thermal Unit Commitment Problem journal, August 2006

Lotsizing with backlogging and start-ups: the case of Wagner–Whitin costs journal, September 1999

A genetic algorithm modelling framework and solution technique for short term optimal hydrothermal scheduling journal, May 1998

A new method for unit commitment with ramping constraints journal, July 2002

Unit commitment by simulated annealing journal, January 1990

A Chance-Constrained Two-Stage Stochastic Program for Unit Commitment With Uncertain Wind Power Output journal, February 2012

Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints journal, August 2006

Min-up/min-down polytopes journal, June 2004

A solution to the unit commitment problem—a review journal, April 2013

Solving the Unit Commitment Problem by a Unit Decommitment Method journal, June 2000

A genetic algorithm solution to the unit commitment problem journal, January 1996

Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem journal, February 2012

Lower Bounds in Lot-Sizing Models: A Polyhedral Study journal, February 1998

Tight and Compact MILP Formulation of Start-Up and Shut-Down Ramping in Unit Commitment journal, May 2013

Dynamic Programming Approach to Unit Commitment journal, January 1987

The Next Generation of Electric Power Unit Commitment Models book, January 2001

Min-up/Min-down Polytopes text, January 1982

Dynamic Programming Approach to Unit Commitment journal, May 1987

Tight and compact MILP formulation for the thermal unit commitment problem conference, July 2015

Tight and compact MILP formulation of start-up and shut-down ramping in unit commitment conference, January 2013

Integer and Combinatorial Optimization journal, September 1989

Min-up/Min-down Polytopes text, January 1982

Integer and Combinatorial Optimization journal, February 1990

A Branch-and-Bound Algorithm for Unit Commitment journal, February 1983

Tight MIP formulations for bounded up/down times and interval-dependent start-ups journal, October 2016

Lifted polymatroid inequalities for mean-risk optimization with indicator variables journal, January 2019

Parallel matheuristics for the discrete unit commitment problem with min-stop ramping constraints journal, May 2018

Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables preprint, January 2017

Solving unit commitment problems with general ramp constraints
journal, June 2008

Tighter Approximated MILP Formulations for Unit Commitment Problems
journal, February 2009

Unit commitment literature synopsis
journal, January 1994

Generating Unit Commitment by Dynamic Programming
journal, May 1966

A strong conic quadratic reformulation for machine-job assignment with controllable processing times
journal, May 2009

Tight and Compact MILP Formulation for the Thermal Unit Commitment Problem
journal, November 2013

Decomposition approach to problem of unit commitment schedule for hydrothermal systems
journal, January 1980

Production Smoothing with Fluctuating Price
journal, January 1975

A Tutorial on Production Smoothing and Work Force Balancing
journal, December 1967

Optimal planning of cogeneration production with provision of ancillary services
journal, February 2013

A Branch-and-Bound Algorithm for Unit Commitment
journal, February 1983

Unit commitment by tabu search
journal, January 1998

An effective heuristic for combined heat-and-power production planning with power ramp constraints
journal, March 2007

A Computationally Efficient Mixed-Integer Linear Formulation for the Thermal Unit Commitment Problem
journal, August 2006

Lotsizing with backlogging and start-ups: the case of Wagner–Whitin costs
journal, September 1999

A genetic algorithm modelling framework and solution technique for short term optimal hydrothermal scheduling
journal, May 1998

A new method for unit commitment with ramping constraints
journal, July 2002

Unit commitment by simulated annealing
journal, January 1990

A Chance-Constrained Two-Stage Stochastic Program for Unit Commitment With Uncertain Wind Power Output
journal, February 2012

Solving Nonlinear Single-Unit Commitment Problems with Ramping Constraints
journal, August 2006

Min-up/min-down polytopes
journal, June 2004

A solution to the unit commitment problem—a review
journal, April 2013

Solving the Unit Commitment Problem by a Unit Decommitment Method
journal, June 2000

A genetic algorithm solution to the unit commitment problem
journal, January 1996

Tight Mixed Integer Linear Programming Formulations for the Unit Commitment Problem
journal, February 2012

Lower Bounds in Lot-Sizing Models: A Polyhedral Study
journal, February 1998

Tight and Compact MILP Formulation of Start-Up and Shut-Down Ramping in Unit Commitment
journal, May 2013

Dynamic Programming Approach to Unit Commitment
journal, January 1987

The Next Generation of Electric Power Unit Commitment Models
book, January 2001

Min-up/Min-down Polytopes
text, January 1982

Dynamic Programming Approach to Unit Commitment
journal, May 1987

Tight and compact MILP formulation for the thermal unit commitment problem
conference, July 2015

Tight and compact MILP formulation of start-up and shut-down ramping in unit commitment
conference, January 2013

Integer and Combinatorial Optimization
journal, September 1989

Min-up/Min-down Polytopes
text, January 1982

Integer and Combinatorial Optimization
journal, February 1990

A Branch-and-Bound Algorithm for Unit Commitment
journal, February 1983

Tight MIP formulations for bounded up/down times and interval-dependent start-ups
journal, October 2016

Lifted polymatroid inequalities for mean-risk optimization with indicator variables
journal, January 2019

Parallel matheuristics for the discrete unit commitment problem with min-stop ramping constraints
journal, May 2018

Lifted Polymatroid Inequalities for Mean-Risk Optimization with Indicator Variables
preprint, January 2017