Tactical models for hierarchical capacitated lot-sizing problems with set-ups and changovers

In this paper, we propose a modelling approach for the medium term planning of manufacturing systems characterized by coexisting large volume and small volume products, in which changeovers play a critical role in achieving maximum efficiency. Although the model is based upon the large time bucket paradigm, it is capable of representing start-ups by sequencing the lots of items produced in long sequences. Specifically, we consider a capacitated lot-sizing problem with parallel machines, in which the products have a three-level hierarchical structure; end items are aggregated into families, which in turn are aggregated into types. Minor set-ups and major changeovers take place when switching between families within a type or between types, respectively. The resulting mathematical programming problem is decomposed via Lagrangean relaxation, leading to sub-problems that can be solved in polynomial time. The whole approach has been validated by applying it to large size case studies drawn from the textile industry.