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An algorithm for binary linear chance-constrained problems using IIS

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Abstract

We propose an algorithm based on infeasible irreducible subsystems to solve binary linear chance-constrained problems with random technology matrix. By leveraging on the problem structure we are able to generate good quality upper bounds to the optimal value early in the algorithm, and the discrete domain is used to guide us efficiently in the search of solutions. We apply our methodology to individual and joint binary linear chance-constrained problems, demonstrating the ability of our approach to solve those problems. Extensive numerical experiments show that, in some cases, the number of nodes explored by our algorithm is drastically reduced when compared to a commercial solver.

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Authors and Affiliations

  1. Universidad Adolfo Ibañez, Diagonal Las Torres 2640, 7941169, Santiago, Chile

    Gianpiero Canessa

  2. AT Kearney Inc, 227 West Monroe Street, Chicago, IL, 60606, USA

    Julian A. Gallego

  3. Texas A&M University, 3131 TAMU, Office ETB 4008, College Station, TX, 77843, USA

    Lewis Ntaimo

  4. Universidad Adolfo Ibañez, Diagonal Las Torres 2640 Oficina 533-C, 7941169, Santiago, Chile

    Bernardo K. Pagnoncelli

  5. IEMS Department, Northwestern University, 2145 Sheridan Road Tech C216, Evanston, IL, 60208-3109, USA

    Bernardo K. Pagnoncelli

Authors
  1. Gianpiero Canessa
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  2. Julian A. Gallego
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  3. Lewis Ntaimo
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  4. Bernardo K. Pagnoncelli
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Correspondence to Gianpiero Canessa.

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Pagnoncelli and Canessa thank the support of Anillo Grant ACT 1407 and Piensa Mineria 2018 Grant.

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Canessa, G., Gallego, J.A., Ntaimo, L. et al. An algorithm for binary linear chance-constrained problems using IIS. Comput Optim Appl 72, 589–608 (2019). https://doi.org/10.1007/s10589-018-00055-9

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  • DOI: https://doi.org/10.1007/s10589-018-00055-9

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