Cyclic Productions planning

We study in this paper the flexible manufacturing systems (FMS) short-term planning problem. It consists of decomposing the initial demand in different cyclic steady states to reduce the complexity of the general planning and scheduling problem. The main criterion to optimize is the makespan. We give a mathematical formulation of the short-term planning problem using cyclic production. However the resulting problem is a non-linear one with integer variables and non linear constraints. To solve the problem, we first make linear the model by generating a database enumerating all the possible cyclic production horizons and their characteristics. Therefore, the remaining variables are the number of steady states, their characteristics (production) and the number of cycles. We have developed an enumerative method which provides, under several assumptions, the optimal solution. We compare then our results with those obtained by the Ohl´s approach (1994) and show that the method developed in this paper provides good results