I am doing a research about the load balancing problem in 5G system, but I am not sure if my problem is a NP-complete problem.
The problem is:
- given a set of n items and a set of m knapsack
- capacity of knapsacks are equal
- the weight of item j in knapsack i is w[i][j],that means weight of a item in each knapsack are different
- each profit of items are equal
I am not trying to put all item in least knapsack like bin packing problem. I saw some similar question answered, but no one is identical to this case. In this case, the goal is to put as more as possible item with m knapsacks. Is the problem a NP-complete problem?