유한 정수 변수를 포함한 가변용량 (0,1)-배낭문제에 대한 절단평면

In this paper, we propose an effective cut generation method based on the Chvatal-Gomory procedure for a variable-capacity (0,1)-Knapsack problem, which is the same problem as the ordinary binary knapsack problem except that a binary capacity variable is newly introduced. 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 show that there exists a pseudopolynomial time algorithm to solve the separation problem. Preliminary computational results are presented which show the effectiveness of the proposed cut generation method.