Column-Randomized Linear Programs: Performance Guarantees and Applications

Abstract

Solving Large-Scale Linear Programs by Randomly Sampling Columns Large-scale linear programs (LPs) play a pivotal role in various applications, including the classic cutting-stock problem and the vehicle routing problem. The standard solution approach for these LPs, namely, column generation (CG), is often computationally intractable because of the NP-hard nature of the corresponding subproblem in many applications. In “Column-Randomized Linear Programs: Performance Guarantees and Applications,” Akchen and Mišić introduce a randomized method that involves first sampling a set of columns from the original LP and subsequently solving an LP composed of the sampled columns, termed the column-randomized LP. The authors analyze the optimality gap of the column-randomized LPs and establish conditions under which the gap is small. Empirical findings demonstrate the effectiveness of the column-randomized LP approach, showcasing its advantages over the CG approach in two practical applications: the cutting-stock problem and nonparametric choice model estimation.