Exact and heuristic algorithms for minimizing the makespan on a single machine scheduling problem with sequence-dependent setup times and release dates

Abstract

This paper proposes efficient exact and heuristic approaches for minimizing the makespan on a single machine scheduling problem with sequence-dependent setup times and release dates. The exact procedure consists of a branch-and-price (B&P) algorithm implemented over an arc-time-indexed formulation with a pseudo-polynomial number of variables and constraints. Our B&P algorithm includes several modern features, such as a dynamic ng-path relaxation and a bidirectional labeling method for efficiently solving the pricing subproblem. The proposed heuristic algorithm is based on the iterated local search framework that employs a beam search approach adapted from the literature for generating initial solutions and an efficient scheme to perform move evaluations in amortized constant time. Computational experiments were carried out on benchmark instances containing 1800 instances ranging from 25 to 150 jobs. The results obtained attest the high performance of both the exact and heuristic algorithms in obtaining high-quality bounds when compared to existing methods. We report improved lower and upper bounds for the vast majority of the instances, as well as optimal solutions for 42.7% of the instances.