On the Resource Allocation Problem with S-Shaped Utility Functions.
CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF OPERATIONS RESEARCH
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A given amount a of a resource is allocated among n activities. A return F sub i x sub i is obtained as a result of using x sub i units of the resource in activity i. The problem is to find an allocation which maximizes the total return, that is, max. the summation from i 1 to n F sub i x sub i S.T. the summation from i 1 to n x sub i a, x sub i or 0. In the paper one examines this well known problem under the assumption that the F sub is are s-shaped functions. In an economic context this assumption means that small allocations lead to essentially zero returns while large ones have a saturation effect, the law of diminishing returns. The same shape may arise when the F sub is are distribution functions. An example of this latter case connected to an inventory problem is provided in the appendix to this paper. Author
- Operations Research