A Flow shop Production Planning Problem with basic period policy and Sequence Dependent set up times

Many authors have examined lot sizing, scheduling and sequence of multi-product flow shops, but most of them have assumed that set up times are independent of sequence. whereas dependence of set up times to sequence is more common in practice. hence, in this paper, we examine the discussed problem with hypothesis of dependence of set up times to sequence and cyclic schedule policy in basic period form. to do so, a mixed integer non-linear programming (nlp) model is developed for this problem. to solve the model these techniques are applied: heuristic g-group for determining the frequency of item production and assigning product to periods and three meta heuristic methods including hybrid particle swarm optimization , hybrid vibration damping optimization hybrid genetic algorithm are used to determine the sequence and economic lot sizes of each item. in addition, to compare these methods, some random problems are produced and computation of them shows the substantial superiority of hybrid particle swarm optimization.