Demand forecasting, lot sizing and scheduling on a rolling horizon basis

Lot sizing and scheduling problems arise when a variety of products are manufactured in a plant of finite capacity in which a single product variant at one time can be manufactured, and changeover costs (and/or times) depend on the products scheduling sequence. MIP models developed to solve these problems are hard to be optimally solved, essentially for the relevant number of integer variables required to represent all possible changeovers in the planning horizon. However, in many real applications, production is planned on a rolling horizon basis, that is, only decisions related to the first period of the planning horizon are usually implemented. Production decisions on later periods are often only represented, because these are obtained using data (forecasted demand) that will change in the next period. Thus, it is not worth spending a lot of time to exactly solve a problem whose input data are imprecise and unstable because to do so would be to exactly solve the wrong problem. This suggests the formulation of simplified models that do not consider the scheduling sequences in later periods. In this paper it is shown that if on one hand demand uncertainty due to forecasting justifies the model simplification (making it senseless to specify the exact future scheduling sequences) then on the other hand it introduces instability issues that can have a considerable impact on the performances of simplified MIP formulations. The study is conducted using data from a real case and simulating both the demand forecasting procedure and the production planning phase on a rolling horizon basis, and gives insights for deciding on the appropriate level of simplification of MIP formulations that can be successfully applied to these problems.