Simultaneous lot-sizing and scheduling in flexible job shop problems

Procurement lot-sizing and production scheduling are as the two critical factors on controlling system costs. This paper considers a particular problem of integrated lot-sizing and scheduling for several products in capacitated flexible job shop configuration, taking into account sequence-dependent setup time. First, a novel mixed integer programming (MIP) model, based on big bucket time models, is proposed to formulate the problem. Then, in order to overcome the complexity of this model, a new hybrid algorithm which combines the genetic algorithm (GA), particle swarm optimization algorithm (PSO), and a local search heuristic is developed. The applicability of GA to solving problems with discrete variables and the efficacy of PSO to tackling problems with continuous variables is the motivation for applying the combination of these algorithms to the investigated problem which has both discrete and continuous solution space. The Taguchi method is used in order to calibrate the simulated annealing algorithm parameters. Then, the efficiency of the proposed algorithms is discussed. The computational results indicated that the proposed algorithm has performed better than the classic GA algorithm and MIP model with respect to both the quality of solutions and computation time.