Introduction to Large‐Scale Linear Programming and Applications

Abstract Linear programming (LP) has been used as an effective tool to solve a number of applications in manufacturing, transportation, military, health care, and finance. In a number of these applications, the problem size in terms of the number of variables and constraints can become rather large in order to accurately represent the system. For this reason, a number of specialized procedures such as column generation and cutting‐plane methods have been developed to effectively solve these large‐scale linear programs. In other cases, the problem may have a special structure, where decomposition methods can also be used. This article provides an overview of these specialized solution procedures. We conclude the article with an example of a large‐scale linear program developed to balance routes for street sweepers in Southern California.