• 산업경영시스템학회지
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• 제21권45호
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• pp.291-299
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• 1998

We present a variant for the generalized continuous multiple-choice knapsack problem[1], which additionally has the well-known generalized lower bound constraints. The presented problem is characterized by some variables which only belong to the simple upper bound constraints and the others which are partitioned into both the continuous multiple-choice constraints and the generalized lower bound constraints. By exploiting some extended structural properties, an efficient algorithm of order Ο($n^2$1og n) is developed, where n is the total number of variables. A numerical example is presented.

• 대한산업공학회지
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• 제23권4호
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• pp.661-667
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• 1997

We consider a generalized problem of the continuous multiple choice knapsack problem and study on the LP relaxation of the candidate problems which are generated in the branch and bound algorithm for solving the generalized problem. The LP relaxed candidate problem is called the generalized continuous multiple choice linear knapsack problem and characterized by some variables which are partitioned into continuous multiple choice constraints and the others which only belong to simple upper bound constraints. An efficient algorithm of order O($n^2logn$) is developed by exploiting some structural properties and applying binary search to ordered solution sets, where n is the total number of variables. A numerical example is presented.