A mixed integer formulation and an efficient metaheuristic for the unrelated parallel machine scheduling problem: Total tardiness minimization

In this paper, the unrelated parallel machine scheduling problem with the objective of minimizing the total tardiness is addressed. For such a problem, a mixed-integer linear programming (MILP) formulation, that considers assignment and positional variables, is presented. In addition, an iterated local search (ILS) algorithm that produces high-quality solutions in reasonable times is proposed for large size instances. The ILS robustness was determined by comparing its performance with the results provided by the MILP. The instances used in this paper were constructed under a new approach which results in tighter due dates than the previous generation method for this problem. The proposed MILP formulation was able to solve instances of up to 150 jobs and 20 machines. Regarding the ILS, it yielded high-quality solutions in a reasonable time, solving instances of a size up to 400 jobs and 20 machines. Experimental results confirm that both approaches are efficient and promising. •A new mixed integer programming formulation for the Unrelated Parallel Machine Scheduling Problem.•The formulation uses positional variables, is linear and does not use the Big-M technique.•The formulation solves instances up to 150 jobs and 20 machines to optimality.•An efficient iterated local search metaheuristic is presented.•A potential issue in the commonly used instance-generation procedure is discussed and a new set of instances is proposed.