particle swarm optimization algorithm for integrated lot-sizing and scheduling in flowshop production environment

production planning and scheduling are the most important issues of the production industries, which have a considerable influence on the productivity of the production systems. although, production planning and scheduling are in two different medium-term and short-term decision making levels, there are a very close relationship between them. ignoring this important feature in production planning aggravates costs and reduces productivity of system. accordingly, in this paper, scheduling constraints have been considered in production planning in order to take into account, the interconnection between these two levels    the purpose of this paper is to study the multi-product and multi-period production systems in the flowshop environement so that the production and scheduling constraints are considered integrated. a more efficient mixed integer programming model with big bucket time approach is proposed to formulate the problem, which can simultaneously achieve a production plan and schedule and that is one of the main novelty of the paper. the objective function includes the cost of production, inventory, shortage and setups. due to the high computational complexity, particle swarm optimization algorithm is proposed to solve the problem. to evaluate the efficiency of the algorithm, two mixed integer programming-based approaches with rolling horizon framework is proposed and the results are compared with each othre. . in addition, taguchi method is used for tunning the parameters of implemented meta-heuristic.the presented algorithms explore the solution space for both lot-sizing and scheduling and find a combination of production plan and sequence that is feasible and close to optimum. computational experiments are performed on randomly generated instances to show the efficiency of the solution methods. computational experiments demonstrate that the performed methods have good-quality results for the test problems. computational experiences show that the proposed algorithms can find good quality solution for the problem in a reasonable time. also, the computational experiences confirm the efficiency of meta-heuristic against exact and heuristic methods. the average of objective value for pso, heuristic 1 and heuristic 2 are 98.21, 104.20 and 108.29 (×103), respectively.