From the Aggregate Plan to Lot-Sizing in Multi-level Production Planning Jean-Claude Hennet LAAS-CNRS , 7 Ave. Colonel Roche, 31077 Toulouse FRANCE 1 INTRODUCTION The hierarchical approach to production planning is classically used to handle the organization and logistics in complex production systems. It distinguishes several decision levels using differ- ent descriptions of the production process. The upper-level planning horizon is relatively long, and, since the number of time intervals (or buckets) of this horizon is restricted by computational limitations, these buckets are long compared with production cycle times. At this time scale, discrete flows in manufacturing plants can be approximated by continuous flows describing pro- duction processes in an aggregated and simplified way. Product flows are generally associated with families of products (Bitran, Tirupati 1993 [?]). In the discrete-time framework used in this study, these flows generate, over each time bucket, important amounts of products, which can be approximately represented by continuous variables. The optimal planned outputs are computed on the basis of forecasted demands and aggregate resource constraints. The results obtained at the aggregate planning level then have to be disaggregated in time and detailed by products and items, taking into account some basic constraints originating from operational levels. As the time horizon is chosen smaller, hard constraints and conflicts increase and continuous variables are less appropriate for describing real phenomena (Agnetis et al. [?]). Other models, of the discrete event type, are needed to schedule production, supplies and sales. Heterogeneous mod- els are obviously hard to combine, and much research effort have been devoted to constructing integrated planning and scheduling schemes (see e.g. Gershwin 1987 [?], Dauz` ere-P´ eres, Lasserre 1994 [?]). The main purpose of this study is to present several continuous models which can be logically sequenced to organize and optimize the implementation of the production decisions taken at the upper planning level. It is shown that, for the set of planning stages, model integration is possible through • time disaggregation, generating a short-term planning problem with small buckets, using the first period results of the longer horizon plan. • product family and aggregate resource disaggregation • decomposition of demands for final products into demands for components through an MRP-type mechanisms, defining multi-stage planning problems. 1 Modeling Manufacturing Systems. From aggregate planning to real-time control, P.Brandimarte, A.Villa Eds, Springer, 1999, pp.5-23, 1999.