in reply to
Re^2: Computer science Problem - single dimension bin packing
in thread Computer science Problem - single dimension bin packing
The Wikipedia article has a section on that:
Multiple knapsack problem
This variation is similar to the Bin Packing Problem. It differs from the Bin Packing Problem in that a subset of items can be selected, whereas, in the Bin Packing Problem, all items have to be packed to certain bins. The concept is that there are multiple knapsacks. This may seem like a trivial change, but it is not equivalent to adding to the capacity of the initial knapsack. This variation is used in many loading and scheduling problems in Operations Research and has a PTAS.
I'm afraid I'm not familiar with this variation, but having a name to search for should help, I reckon.