A hybrid VNS-Lagrangean heuristic framework applied on single machine scheduling problem with sequence-dependent setup times, release dates and due dates

Abstract

In this work, we propose a hybrid VNS-Lagrangean heuristic applied on the single machine scheduling problem with sequence-dependent setup times, release dates, and due dates. The objective function is the minimization of the total tardiness. The proposed hybrid heuristic is a Lagrangean relaxation integrated with the variable neighborhood search (VNS). The methodology can generate strong bounds, using the information of the Lagrangean multipliers to construct and perturb feasible solutions within the VNS framework. We compare its performance with previous hybrid approaches and find that the upper bounds obtained are optimal for several cases and tight for others. The methodology presents competitive results when compared with previous related works.