On an Allocation Problem with Multistage Constraints

This paper gives a simple algorithm for finding optimal allocations subject to a hierarchy of limits when the loss function is separable strictly convex and the resources function is linear. Its applications to capital budgeting and multistage sampling are pointed out. The allocation problem considered by Srikantan [Opns. Res. 11, 265–273 (1963)] is a special case of the problem considered in this paper.