Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
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A Cut Generation Method for the (0, 1)-Knapsack Problem with a Variable Capacity

용량이 변화하는 (0, 1)-배낭문제에 대한 절단평면 생성방안

  • 이경식 (한국전자통신연구원 우정기술연구부) ;
  • 박성수 (한국과학기술원 산업공학과)
  • Published : 2000.09.01
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Abstract

In this paper, we propose a practical cut generation method based on the Chvatal-Gomory procedure for the (0, 1)-Knapsack problem with a variable capacity. For a given set N of n items each of which has a positive integral weight and a facility of positive integral capacity, a feasible solution of the problem is defined as a subset S of N along with the number of facilities that can satisfy the sum of weights of all the items in S. We first derive a class of valid inequalities for the problem using Chvatal-Gomory procedure, then analyze the associated separation problem. Based on the results, we develop an affective cut generation method. We then analyze the theoretical strength of the inequalities which can be generated by the proposed cut generation method. Preliminary computational results are also presented which show the effectiveness of the proposed cut generation method.

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References

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