Evaluation and Incremental Determination of Almost Optimal Allocations of Resources

The problem of allocating resources to activities with strictly concave return functions is considered; the objective function to be maximized is the sum of the returns from each activity. It is demonstrated that any set of feasible allocations can be used to obtain an explicit upper bound of the optimal value of this function. The upper bound is used to check that a numerically fast incremental procedure produces almost optimal allocations. A conservative solution of the allocation problem is generated by successively incrementing allocations with the greatest marginal returns; practical allocations are obtained from the conservative allocations by a method resulting in a reduction of the number of nonzero allocations and a simultaneous increase of the value of the objective function.