Capacity management through Lagrangean relaxation: an application to tyres production

A new integrated approach to capacity management in complex manufacturing systems is developed and the resulting framework is applied to a case study in tyre production. A hierarchical multilayered decomposition of the planning process is proposed, in which lower layers provide an increased level of detail and accuracy in capacity representation and analysis. Thus, a large and comprehensive model describing the manufacturing system is subdivided into smaller sub-models via relaxation and decomposition techniques. The Lagrangean multipliers provide a bi-directional link among different layers, reducing the risk of sub-optimization and infeasibility of the aggregate plans. Each of the sub-models is easier to solve than the original one and involves a different set of decision variables. Moreover, they relate to different levels of the management hierarchy, so that there emerges a strict correspondence between the decomposition scheme and the decision process underlying capacity management.