Minimization of maximum lateness on parallel machines with a single server and job release dates

This paper addresses the problem of scheduling independent jobs with release dates on identical parallel machines with a single server. The goal consists in minimizing the maximum lateness. This is a realistic extension of the traditional parallel machine scheduling problem with a single server, in which all jobs are assumed to be available at the beginning of the schedule. This problem, referred to as $$P,S1|r_j|L_{max}$$ P , S 1 | r j | L max , has various applications in practice. To date, research on it has focused on complexity analysis. To solve small-sized instances of the problem, we present two mixed-integer-programming formulations, along with a valid inequality. Due to the $${\mathcal {N}}{\mathcal {P}}$$ N P -hard nature of the problem, we propose a constructive heuristic and two metaheuristics, namely a General Variable Neighborhood Search (GVNS) and a Greedy Randomized Adaptive Search Procedures, both using a Variable Neighborhood Descent as an intensification operator. In the experiments, the proposed algorithms are compared using a set of new instances generated randomly with up to 500 jobs, in line with the related literature. It turns out that GVNS outperforms by far the other approaches.