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Two-stage robust mixed integer programming problem with objective uncertainty

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Abstract

Many real problems with uncertain parameters can be modeled as two-stage robust mixed integer programming problems (RMIPs). Due to the complex nature of this kind of problems, this paper focuses on the two-stage RMIPs with objective uncertainty. Based on the results that the augmented Lagrangian is a strong dual for integer programming Boland and Eberhard (Math Program 150(2):491–509, 2015), we present the upper and lower bounds. In a special case, we show that the two-stage RMIPs can be equivalently reformulated as a solvable minimax problem.

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Acknowledgements

The research published here was conducted at the Future Resilient Systems at the Singapore-ETH Centre (SEC). The SEC was established as a collaboration between ETH Zurich and National Research Foundation (NRF) Singapore (FI 370074011) under the auspices of the NRF’s Campus for Research Excellence and Technological Enterprise (CREATE) programme. The author wish to thank referees for their insightful comments which have helped improve the quality of this paper. She also wants to thank Professor Defeng Sun and Dr. Aakil M. Caunhye from National University of Singapore and Future Resilient Systems, Singapore-ETH Centre for their suggestions of revising this paper.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore

    Ning Zhang

  2. Future Resilient Systems, Singapore ETH Centre, 1 Create Way, CREATE Tower, Singapore, 138602, Singapore

    Ning Zhang

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  1. Ning Zhang
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Correspondence to Ning Zhang.

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Zhang, N. Two-stage robust mixed integer programming problem with objective uncertainty. Optim Lett 12, 959–969 (2018). https://doi.org/10.1007/s11590-017-1176-z

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  • DOI: https://doi.org/10.1007/s11590-017-1176-z

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