Let be a partition of , be a partition of and and are scalars for . We consider the problem: Minimise subject to , , to and to , . An algorithm is proposed to solve this problem. We also obtain a linear time 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 algorithm to solve the continuous minimax kanpsack problem with GLB constraints which improves the existing time bound.
