From the Aggregate Plan to Lot-Sizing in Multi-level Production Planning

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 different 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 production 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 models are obviously hard to combine, and much research effort have been devoted to constructing integrated planning and scheduling schemes (see e.g. Gershwin 1987 [?], Dauzère-Péres, Lasserre 1994 [?]).