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

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.