IMACS Multiconference on "Computational Engineering in Systems Applications"(CESA), October 4-6, 2006, Beijing, China. Cyclic Productions planning Ouajdi Korbaa, Herve Camus Lagis - Ecole Centrale de Lille BP 48 - Cite Scientifique F-5965 1 Villeneuve d'Ascq cedex - France Phone: +33 3 20 33 54 52, Fax: +33 3 20 33 54 18, E-mail: Abstract - 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 [OHL 94] and show that the method developed in this paper provides good results. Keywords: FMS, short-term planning problem, cyclic behavior, steady states, makespan minimization. I. INTRODUCTION Today, much attention of both management scientists and practitioners is given to the hierarchical planning systems. These systems are often decomposed into three decision- making levels: a medium term level, a short term level and a very short term level [XIE 87]. The medium term level balances the expected production in order to avoid overload periods. It has been widely studied and was the subject of different studies [XIE 87], [BAH 99], [OUE 99]. The short term planning decomposes effective demand into "schedulable" sets in order to respect workshop constraints [STE 88], [STE 91], [STE 92] and [OHL 94]: computation of cyclic production with different steady states if necessary. As for the very short term level, it consists of evaluating the real performances of the production system scheduling the steady states production [HIL 89], [VAL 94], [OHL 95] and [KOR 02] and taking into account the transient states for cyclic production [KOR 01] and [KOR 03], which is not possible during the short term planning problem. In this paper we focus on the short-term production planning. Therefore, we suppose that demand is known and that the product structures and capacity requirements have been _, herve.camusgec-lille.fr expressed in terms of product groups and machine groups. These information are provides by the upper lever by using MRP (Manufacturing Resource Planning) system for example [XIE 87]. Consequently, we know the due quantity of part type and its operating sequence (description of the manufacturing process in terms of operations sequence to perform the part). A Flexible Manufacturing System (FMS) consists of a set of workstations capable of performing a number of different operations and connected by a transportation mechanism. It produces simultaneously different part types. The flexibility of the system allows the choice of one or more stations for each operation and one or more processes to manufacture each part type. The reason of such a choice is that FMS represents the best compromise between flexibility and economical cost for this type of production (small or medium). For the FMS control, we have adopted a cyclic behavior for several reasons. Cyclic scheduling offers to optimize simultaneously different criteria (work in process, workflow, etc). It decomposes the complexity of the general planning and scheduling problem (NP-Hard problem). Such schedule can react rapidly in the particular case of an unexpected increase of the production: we just have to repeat the cycle as long as needed. In addition, in case of including a non planned high priority production, the computation of including this new production into the provisional production costs less time and this production can be introduced in the FMS more rapidly. Indeed, the smaller the production cycle is, the shorter time it takes to schedule it and the shorter time it takes to end without loss the steady state. So, by adopting this type of behavior, we'll make scheduling step easier. Finally the survey of such a production is easier using small cyclic production repeated a lot of times. In our case, the short-term production planning has to determine one or several steady cyclic and deterministic states to achieve production. As we work with discrete variables and non continuous variables, we have to think about possible discontinuous performance using several different cyclic steady states. During each state, the cycle is repeated until the expected production is performed. Among the objective of establishing of one or more steady states, we have the optimization of quantitative criteria like balancing the workloads of the machines, maximizing the number of part types to produce simultaneously in a steady state, minimizing the makespan, etc. 1110