Mathematical Programming

, Volume 157, Issue 1, pp 277–296 | Cite as

Robust optimization approach for a chance-constrained binary knapsack problem

  • Jinil Han
  • Kyungsik Lee
  • Chungmok Lee
  • Ki-Seok Choi
  • Sungsoo Park
Full Length Paper Series B


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.


Knapsack problem Combinatorial optimization Chance-constrained programming Robust optimization 

Mathematics Subject Classification

90C15 90C27 90C59 



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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Copyright information

© Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society 2015

Authors and Affiliations

  1. 1.CORE, Université catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Department of Industrial and Systems EngineeringKorea Advanced Institute of Science and TechnologyDaejeonRepublic of Korea
  3. 3.Department of Industrial Engineering & Institute for Industrial Systems InnovationSeoul National UniversitySeoulRepublic of Korea
  4. 4.Department of Industrial and Management EngineeringHankuk University of Foreign StudiesGyeonggi-doRepublic of Korea

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