Using a variable neighborhood search to solve a bi-objective identical parallel machine scheduling problem

We developed a variable neighborhood search heuristic and a mixed integer programming model for the identical parallel machine scheduling problem with sequence dependent setup time. For this problem, we consider minimizing two objectives, which are the makespan and the flow time. The heuristic proposed has a constructive procedure to build initial solutions, five neighborhood structures, and a local search based on the variable neighborhood descent. Computational experiments indicate that the heuristic is very fast and can return better solutions than the model since it found 90% of the best solutions. It also outperformed all solutions computed with the longest processing time and the shortest processing time rules, both commonly adopted for scheduling problems.