The p-dimensional vector packing problem, also called general assignment problem, is a generalization of bin packing with multiple constraints. In this problem, we are required to pack n items of m different types, represented by p-dimensional vectors, into as few bins as possible.

In practice, this problem models, for example, static resource allocation problems where the minimum number of servers with known capacities is used to satisfy a set of services with known demands. The multiple-choice vector bin packing problem is a variant of the vector packing problem in which bins have several types (i.e., sizes and costs) and items have several incarnations (i.e., will take one of several possible sizes).