Practical guidelines for solving difficult linear programs

The advances in state-of-the-art hardware and software have enabled the inexpensive, efficient solution of many large-scale linear programs previously considered intractable. However, a significant number of large linear programs can require hours, or even days, of run time and are not guaranteed to yield an optimal (or near-optimal) solution. In this paper, we present suggestions for diagnosing and removing performance problems in state-of-the-art linear programming solvers, and guidelines for careful model formulation, both of which can vastly improve performance.

► We provide background on linear programming.
► We give insights as to why linear programs are difficult to solve.
► We describe ways to resolve performance problems with linear programs.