Accession Number : AD0726886
Title : On the Resource Allocation Problem with S-Shaped Utility Functions.
Descriptive Note : Technical memo.,
Corporate Author : CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF OPERATIONS RESEARCH
Personal Author(s) : Vicentini,Fabio M.
Report Date : AUG 1970
Pagination or Media Count : 13
Abstract : 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 i's 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 i's are distribution functions. An example of this latter case connected to an inventory problem is provided in the appendix to this paper. (Author)
Descriptors : (*INVENTORY CONTROL, MATHEMATICAL MODELS), DISTRIBUTION FUNCTIONS, SET THEORY, NUMERICAL ANALYSIS, OPTIMIZATION
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE