• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.1
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• pp.31-41
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• 1992

An extension of generalized linear multiple choice knapsack problem [1] is presented and an algorithm of order 0([n .n$_{max}$]$_{2}$) is developed by exploiting its extended properties, where n and n$_{max}$ denote the total number of variables and the cardinality of the largest multiple choice set, respectively. A numerical example is presented and computational aspects are discussed.sed.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.4
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• pp.519-527
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• 1995

By finding some new properties, we develop an O($r_{max}n^2$) algorithm for the generalized multiple choice linear knapsack problem where $r_{max}$ is the largest multiple choice number and n is the total number of variables. The proposed algorithm can easily be embedded in a branch-and-bound procedure due to its convenient structure for the post-optimization in changes of the right-hand-side and multiple choice numbers. A numerical example is presented.

• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.3
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• pp.1-9
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• 1997

We present an extension of the well-known generalized upper bound (GUB) constraint and consider a linear knapsack problem with both the extended GUB constraints and the simple upper bound (SUB) constraints. An efficient algorithm of order O($n^2log n$) is developed by exploiting structural properties and applying binary search to ordered solution sets, where n is the total number of variables. A numerical example is presented.