Continuous flow models for batch manufacturing: A basis for a hierarchical approach

In this paper the authors propose approximate dynamic models, based on continuous material flows, in order to overcome the difficulties usually faced by classical machine scheduling methods, such as computational complexity, limited ability to model all the features of real manufacturing environments and to cope with unpredictable events. The continuous flow approach, which has been often proposed for repetitive manufacturing environments, is exploited here for a batch manufacturing environment; a multi-stage case is used to illustrate the methodology. Both discrete and continuous time dynamic models are considered. Some computational complexity results are given for the resulting optimization problems. Based on these models, a two-level hierarchical approach is proposed: the task of the upper hierarchical level is to solve the continuous flow scheduling problem, yielding a reference production trajectory; the task of the lower level is detail scheduling, aimed at meeting the production targets set by the upper level. Constraints may be added to the continuous flow model in order to cope with unfeasibilities detected by the lower level, resulting in a two-way hierarchical scheme.