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Tight MIP Formulations for Bounded Up/Down Times and Interval-Dependent Start-Ups

Author

Listed:
  • Queyranne, M.

    (Université catholique de Louvain, CORE, Belgium)

  • Wolsey, L.A.

    (Université catholique de Louvain, CORE, Belgium)

Abstract

Switching machines on and off is an important aspect of unit commitment problems and production planning problems, among others. Here we study tight mixed integer programming formulations for two aspects of such problems: bounded length on- and off-intervals, and interval-dependent start-ups. For the problem with both these aspects we develop a tight (convex hull) formulation involving additional variables. For the bounded interval problem we present a tight network dual formulation based on new integer variables that allows us to simultaneously treat lower and upper bounds on the interval lengths. This in turn leads to more general results, including simpler proofs of known tight formulations for problems with just lower bounds. For the interval-dependent start-up problem we develop a path formulation that allows us to describe the convex hull of solutions in the space of machine-on and interval-dependent start-up variables.

Suggested Citation

  • Queyranne, M. & Wolsey, L.A., 2015. "Tight MIP Formulations for Bounded Up/Down Times and Interval-Dependent Start-Ups," LIDAM Discussion Papers CORE 2015036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2015036
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2015.html
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    References listed on IDEAS

    as
    1. Fujita,Masahisa & Thisse,Jacques-François, 2013. "Economics of Agglomeration," Cambridge Books, Cambridge University Press, number 9781107001411.
    2. Queyranne, M. & Wolsey, L.A., 2015. "Modeling poset convex subsets," LIDAM Discussion Papers CORE 2015049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Hindriks, Jean & Myles, Gareth D., 2013. "Intermediate Public Economics," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262018691, December.
    4. Fleurbaey, Marc & Maniquet, François, 2015. "Optimal taxation theory and principles of fairness," LIDAM Discussion Papers CORE 2015005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. NESTEROV, Yurii, 2015. "Complexity bounds for primal-dual methods minimizing the model of objective function," LIDAM Discussion Papers CORE 2015003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Queyranne, M. & Wolsey, L.A., 2015. "Modeling poset convex subsets," LIDAM Discussion Papers CORE 2015049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Stevens, Nicolas & Papavasiliou, Anthony, 2022. "Application of the Level Method for Computing Locational Convex Hull Prices," LIDAM Discussion Papers CORE 2022002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

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    More about this item

    Keywords

    production sequencing; unit commitment; bounded up/down times; interval-dependent startups; tight MIP formulations; convex hulls;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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