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http://dx.doi.org/10.7232/JKIIE.2011.37.3.258

On a Two Dimensional Linear Programming Knapsack Problem with the Generalized GUB Constraint  

Won, Joong-Yeon (Industrial and Management Engineering, Kyonggi University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.37, no.3, 2011 , pp. 258-263 More about this Journal
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.
Keywords
Generalized GUB Constraint; Two Dimensional LP Knapsack Problem; Computational Complexity;
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  • Reference
1 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.
2 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.   DOI   ScienceOn
3 Kronsjo, L. I. (1979), Algorithms : Their Complexity and Efficiency, Wiley, N. Y.