Flowshop sequence-dependent group scheduling with minimisation of weighted earliness and tardiness

In this research, we approach the flowshop sequence-dependent group scheduling problem with minimisation of total weighted earliness and tardiness as the objective for the first time. A mixed integer linear programming model is developed to solve the problem optimally. Since the proposed research problem is proven to be NP-hard, a hybrid meta-heuristic algorithm based on the particle swarm optimisation (PSO) algorithm, enhanced with neighbourhood search is developed to heuristically solve the problem. Since the objective is a non-regular, a timing algorithm is developed to find the best schedule for each sequence provided by the metaheuristic algorithm. A lower bounding method is also developed by reformulating the problem as a Dantzig-Wolf decomposition model to evaluate the performance of the proposed PSO algorithm. The computational results, based on using available test problems in the literature, demonstrate that the proposed PSO algorithm and the lower bounding method are quite effective, especially in the instances with loose due date.