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http://dx.doi.org/10.7232/JKIIE.2014.40.4.396

The Generalized Multiple-Choice Multi-Divisional Linear Programming Knapsack Problem  

Won, Joong-Yeon (Department of Industrial and Management Engineering, Kyonggi University)
Publication Information
Journal of Korean Institute of Industrial Engineers / v.40, no.4, 2014 , pp. 396-403 More about this Journal
Abstract
The multi-divisional knapsack problem is defined as a binary knapsack problem where each mutually exclusive division has its own capacity. In this paper, we present an extension of the multi-divisional knapsack problem that has generalized multiple-choice constraints. We explore the linear programming relaxation (P) of this extended problem and identify some properties of problem (P). Then, we develop a transformation which converts the problem (P) into an LP knapsack problem and derive the optimal solutions of problem (P) from those of the converted LP knapsack problem. The solution procedures have a worst case computational complexity of order $O(n^2{\log}\;n)$, where n is the total number of variables. We illustrate a numerical example and discuss some variations of problem (P).
Keywords
The Multi-Divisional Knapsack Problem; Generalized Multiple-Choice Constraints; Computational Complexity;
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Times Cited By KSCI : 3  (Citation Analysis)
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