The resource allocation problem with feedback

This paper treats a new type of resource allocation problem. In this problem we consider resources allocated to activities or consumed at activities as inputs and their effectiveness functions values as outputs. Some proportion of the outputs are returned to the inputs which also consume the resources. We name this the resource allocation problem with feedback. We consider two cases. The former case allows resources to divide into any fraction while in the latter case allocated resources are restricted to whole numbers. The former case naturally yields maximizing a concave objective over a non-convex region. However, it is shown that it can be easily reduced to a convex program. The latter case yields an NP-hard problem. It is shown that it can be solved by dynamic programming.