Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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On a Two Dimensional Linear Programming Knapsack Problem with the Generalized GUB Constraint

일반화된 일반상한제약을 갖는 이차원 선형계획 배낭문제 연구

  • Won, Joong-Yeon (Industrial and Management Engineering, Kyonggi University)
  • 원중연 (경기대학교 산업경영공학과)
  • Received : 2011.05.28
  • Accepted : 2011.08.13
  • Published : 2011.09.01
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Abstract

We study on a generalization of the two dimensional linear programming knapsack problem with the extended GUB constraint, which was presented in paper Won(2001). We identify some new parametric properties of the generalized problem and derive a solution algorithm based on the identified parametric properties. The solution algorithm has a worst case time complexity of order O($n^2logn$), where n is the total number of variables. We illustrate a numerical example.

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References

  1. Bagchi, A., Bhattacharyya, N., and Chakravarti, N. (1996), LP Relaxation of the Two Dimensional Knapsack Problem with Box and GUB Constraints, European J. Opnl. Res., 89, 609-617. https://doi.org/10.1016/0377-2217(94)00285-1
  2. Kronsjo, L. I. (1979), Algorithms : Their Complexity and Efficiency, Wiley, N. Y.
  3. Won, J. Y. (2001), On a Two Dimensional Linear Programming Knapsack Problem with the Extended GUB Constraint, Journal of the Korean Institute of Industrial Engineers, 27(1), 25-29.

Cited by

  1. The Generalized Multiple-Choice Multi-Divisional Linear Programming Knapsack Problem vol.40, pp.4, 2014, https://doi.org/10.7232/JKIIE.2014.40.4.396