Given a set of $n$ numbers, representing quantities of a given product in pallets
I have to fulfill an order of $k$ pieces
order : 165 pallets: [ 150, 20, 5, 50, 80, 120, 15, 10 ]
I want to find the partition which:
1. sums up to at least 165 but contains as little pallets as possible.
2. has minimum cardinality
1 : [150, 20] sum: 170, cardinality 2 2 : [150, 10, 5] sum: 165, cardinality 3 3 : [150, 15] sum: 165, cardinality 2 3 is chosen.
Can you give a name to this mathematical problem?
Is there a fast algorithm, even with approximation?