Accelerating mathematical programming techniques with the corridor method

Abstract

In this paper we investigate how the Benders decomposition, Lagrangean relaxation, and Dantzig–Wolfe reformulation techniques can be accelerated when intertwined with the corridor method. We test the approaches on the capacitated lot sizing problem with setups. Due to the computational complexity of this lot sizing problem, one would expect to find a number of approaches based on decomposition techniques in the literature. While this is true for Lagrangean relaxation and Dantzig–Wolfe reformulation, we could not find any paper proposing the use of Benders decomposition for the problem at hand. Consequently, with this study, we pursue a two-fold goal: First, and foremost, we want to determine how effective the corridor method is as acceleration scheme for these decomposition techniques; second, we aim at gaining some insight into why Benders has not been proposed for this class of problems. Our results shed light on both issues. On the one hand, we show that all the decomposition methods benefit from the hybridisation with the corridor method. On the other hand, a thorough analysis on the behaviour and limitations of Benders algorithm is provided. We conclude the study with a statistical analysis to determine whether significant differences in performance among the different implementations arise.