Some exact algorithms for the knapsack sharing problem

The knapsack sharing problem (KSP) is formulated as an extension to the ordinary knapsack problem. The KSP is NP-hard. We present a branch-and-bound algorithm and a binary search algorithm to solve this problem to optimality. These algorithms are implemented and computational experiments are carried out to analyse the behavior of the developed algorithms. As a result, we find that the binary search algorithm solves KSPs with up to 20 000 variables in less than a minute in our computing environment.