Metaheuristic algorithms for the multistage hybrid flowshop scheduling problem

We consider the multistage hybrid flowshop scheduling problem, in which each stage consists of parallel identical machines. The problem is to determine a schedule that minimizes the makespan for a given set of jobs over a finite planning horizon. Since this problem class is NP-hard in the strong sense, there seems to be no escape from appealing to heuristic procedures to achieve near-optimal solutions to real life problems. First, a series of new global lower bounds to be used to estimate the minimum makespan are derived. Then, two new metaheuristic algorithms first sequence and then allocate jobs to machines based on a particular partition of the shop. The optimization procedure is based on simulated annealing and the variable-depth search. Computational experiments show the efficiency of the proposed procedures.