Journal of Korean Institute of Industrial Engineers (대한산업공학회지)

Korean Institute of Industrial Engineers (대한산업공학회)
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The Generalized Multiple-Choice Multi-Divisional Linear Programming Knapsack Problem

일반 다중선택 다분할 선형계획 배낭문제

  • Won, Joong-Yeon (Department of Industrial and Management Engineering, Kyonggi University)
  • 원중연 (경기대학교 산업경영공학과)
  • Received : 2014.04.15
  • Accepted : 2014.06.26
  • Published : 2014.08.15
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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).

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References

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