Research Reports from the Department of Operations
Document Type
Report
Publication Date
8-1-1970
Abstract
A given amount "a" of a resource is allocated among n activities. A return Fi(xi) is obtained as a result of using xi units of the resource in activity "i". The problem is to find an allocation which maximizes the total return, that is, max Σ Fi(xi) s.t. Σ xi = a, xi ≥ 0 . In this paper we examine this well known problem under the assumption that the Fi'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 Fi's are distribution functions. An example of this latter case connected to an inventory problem is provided in the appendix to this paper.
Keywords
Operations research, Mathematical optimization, Inventory control, Budget, Research and development projects
Publication Title
Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University
Issue
Technical memorandum no. 201
Rights
This work is in the public domain and may be freely downloaded for personal or academic use
Recommended Citation
Vicentini, Fabio M., "On the Resource Allocation Problem with S-Shaped Utility Functions" (1970). Research Reports from the Department of Operations. 370.
https://commons.case.edu/wsom-ops-reports/370