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A deterministic bounding procedure for the global optimization of a bi-level mixed-integer problem

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  • Soares, Inês
  • Alves, Maria João
  • Henggeler Antunes, Carlos

Abstract

In this paper, a deterministic bounding procedure for the global optimization of a mixed-integer bi-level programming problem is proposed. The aim has been to develop an efficient algorithm to deal with a case study in the electricity retail market. In this problem, an electricity retailer wants to define a time-of-use tariff structure to maximize profits, but he has to take into account the consumers’ reaction by means of re-scheduling appliance operation to minimize costs. The problem has been formulated as a bi-level mixed-integer programming model.

Suggested Citation

  • Soares, Inês & Alves, Maria João & Henggeler Antunes, Carlos, 2021. "A deterministic bounding procedure for the global optimization of a bi-level mixed-integer problem," European Journal of Operational Research, Elsevier, vol. 291(1), pages 52-66.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:1:p:52-66
    DOI: 10.1016/j.ejor.2020.09.015
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    References listed on IDEAS

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    1. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2017. "A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs," Operations Research, INFORMS, vol. 65(6), pages 1615-1637, December.
    2. Aussel, Didier & Brotcorne, Luce & Lepaul, Sébastien & von Niederhäusern, Léonard, 2020. "A trilevel model for best response in energy demand-side management," European Journal of Operational Research, Elsevier, vol. 281(2), pages 299-315.
    3. Zeynep Gümüş & Christodoulos Floudas, 2005. "Global optimization of mixed-integer bilevel programming problems," Computational Management Science, Springer, vol. 2(3), pages 181-212, July.
    4. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
    5. Alexander Mitsos, 2010. "Global solution of nonlinear mixed-integer bilevel programs," Journal of Global Optimization, Springer, vol. 47(4), pages 557-582, August.
    6. Soares, Inês & Alves, Maria João & Antunes, Carlos Henggeler, 2020. "Designing time-of-use tariffs in electricity retail markets using a bi-level model – Estimating bounds when the lower level problem cannot be exactly solved," Omega, Elsevier, vol. 93(C).
    7. Zugno, Marco & Morales, Juan Miguel & Pinson, Pierre & Madsen, Henrik, 2013. "A bilevel model for electricity retailers' participation in a demand response market environment," Energy Economics, Elsevier, vol. 36(C), pages 182-197.
    8. James T. Moore & Jonathan F. Bard, 1990. "The Mixed Integer Linear Bilevel Programming Problem," Operations Research, INFORMS, vol. 38(5), pages 911-921, October.
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    Cited by:

    1. Catanzaro, Daniele & Pesenti, Raffaele & Ronco, Roberto, 2021. "Job Scheduling under Time-of-Use Energy Tariffs for Sustainable Manufacturing: A Survey," LIDAM Discussion Papers CORE 2021019, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Catanzaro, Daniele & Pesenti, Raffaele & Ronco, Roberto, 2023. "Job scheduling under Time-of-Use energy tariffs for sustainable manufacturing: a survey," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1091-1109.
    3. Cai, Qiran & Xu, Qingyang & Qing, Jing & Shi, Gang & Liang, Qiao-Mei, 2022. "Promoting wind and photovoltaics renewable energy integration through demand response: Dynamic pricing mechanism design and economic analysis for smart residential communities," Energy, Elsevier, vol. 261(PB).
    4. Oggioni, Giorgia & Schwartz, Alexandra & Wiertz, Ann-Kathrin & Zöttl, Gregor, 2024. "Dynamic pricing and strategic retailers in the energy sector: A multi-leader-follower approach," European Journal of Operational Research, Elsevier, vol. 312(1), pages 255-272.

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