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Robust optimization approach for a chance-constrained binary knapsack problem

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Abstract

We consider a certain class of chance-constrained binary knapsack problem where each item has a normally distributed random weight that is independent of the other items. For this problem we propose an efficient pseudo-polynomial time algorithm based on the robust optimization approach for finding a solution with a theoretical bound on the probability of satisfying the knapsack constraint. Our algorithm is tested on a wide range of random instances, and the results demonstrate that it provides qualified solutions quickly. In contrast, a state-of-the-art MIP solver is only applicable for instances of the problem with a restricted number of items.

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Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (Grant 2011-0027301).

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Authors and Affiliations

  1. CORE, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    Jinil Han

  2. Department of Industrial and Systems Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon, 305-701, Republic of Korea

    Jinil Han & Sungsoo Park

  3. Department of Industrial Engineering & Institute for Industrial Systems Innovation, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 151-742, Republic of Korea

    Kyungsik Lee

  4. Department of Industrial and Management Engineering, Hankuk University of Foreign Studies, San 89, Wangsan-ri, Mohyu-myun, Yongin, Gyeonggi-do, 449-791, Republic of Korea

    Chungmok Lee & Ki-Seok Choi

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  1. Jinil Han
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Correspondence to Kyungsik Lee or Sungsoo Park.

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Han, J., Lee, K., Lee, C. et al. Robust optimization approach for a chance-constrained binary knapsack problem. Math. Program. 157, 277–296 (2016). https://doi.org/10.1007/s10107-015-0931-0

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