simoltaneous lot-sizing and scheduling in hybrid flow shop production environment with resource constraint

the aim of this paper is to study a multi-product, multi-period production systems in a hybrid flow shop so that lot-sizing and scheduling will be detemined simultaneously. a new mixed-integer programming model is proposed to formulate the studied problem. the objective function in this investigation includes the total cost of production, inventory and external supply. in the case of not satisfying the demand of customers, this demand should be met by foreign suppliers with higher price. the simultaneous lot-sizing and scheduling problem are classified in strongly np-hard class. due to the high computational complexity of the studied problem, particle swarm optimization (pso) and imperialist competitive algorithms (ica) are implemented for solving the considered problem. the 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. first, the implemented algorithms are used for solving randomly generated instances with different sizes. then, these methods are used to solve the case of tile industry and the obtained results by two methods are compared with each other. computational experiences show that the algorithms are able to achieve good-quality solutions for the problem in a reasonable time. also, the results of ica are better than pso results for the mentioned case study.