A separable assignment problem (SAP) is defined by a set of bins and a set of items to pack in each bin; a value, f, for assigning item j to bin i; and a separate packing constraint for each bin—i.e., ...

We describe an algorithm for the 0-1 knapsack problem (KP), which relies mainly on three new ideas. The first one is to focus on what we call the core of the problem, namely, a knapsack problem ...