Minmax linear knapsack problem with grouped variables and gub

Abstract

Let be a partition of be a partition of Si and ci and aj are scalars for We consider the problem MinimiseMaximum Subject to An algorithm is proposed to solve this problem. We also obtain a linear tune algorithm to solve the knapsack sharing problem with piece-wise linear trade-off functions which improves its existing time bound. As a by-product of this result, we have an O(n) algorithm to solve the continuous minmax knapsack problem with GLB constraints which improves the existing time bound