allocation problems – Optimization Online

Congressional Apportionment

Published: 2026/08/17

(Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Integer Programming allocation problems, apportionment, MINLP, public sector operations

This book chapter is a gentle introduction to the mathematics of congressional apportionment. It emphasizes the connections between mathematical optimization and the classical apportionment methods (e.g., Jefferson, Adams, Hamilton, Webster, Huntington-Hill, Dean). CitationPrepared for a forthcoming book edited by Bruce Golden and Doug ShierArticleDownload View PDF

On the use of the simplex method for a type of allocation problems

Published: 2018/10/31

Yoshihiro Tanaka

Combinatorial Optimization allocation problems, birkhoff's theorem, hall's theorem, simplex method

In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0-1 integer programming method, H.W. Kuhn [4] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the Birkhoff’s theorem to … Read more