Visualizing and constructing cycles in the simplex method
成果类型：
Article
署名作者：
Avis, David; Kaluzny, Bohdan; Titley-Peloquin, David
署名单位：
McGill University
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1070.0474
发表日期：
2008
页码：
512-518
关键词：
摘要：
Most examples of cycling in the simplex method are given without explanation of how they were constructed. An exception is Beale's example built around the geometry of the dual simplex method in the plane [Beale, E. 1955. Cycling in the dual simplex method. Naval Res. Logist. Quart. 2( 4) 269-275]. Using this approach, we give a simple geometric explanation for a number of examples of cycling in the simplex method, including Hoffman's original example [Hoffman, A. 1953. Cycling in the Simplex Algorithm. National Bureau of Standards, Washington, D. C.]. This gives rise to a simple method for generating examples with cycles.