A Fast Algorithm for the Generalized Multiple Choice Linear Knapsack Problem

일반 다중선택 선형배낭문제의 신속한 해법연구

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.