ECHELON STOCK FORMULATION FOR MULTISTAGE LOT-SIZING WITH COMPONENT LEAD TIMES

Material requirements planning of batch production in multi-stage manufacturing systems is discussed where component parts may have significant non-zero production or purchasing lead time. The presence of such lead time poses a synchronization problem for the rolling horizon planning of component part production in the system. The synchronization problem is analysed, discussed and modelled first for the case of assembly product structures where a component has a unique successor component. The analysis is then extended to the more complex case of general product structures where a component may have multiple successor components. The associated general structure multi-stage lot-sizing problem is then formulated as a mixed integer linear program first in terms of conventional stock, and then reformulated in terms of echelon stock. The echelon stock quantity of a component is its lead-time adjusted total system stock, counted both as a stand-alone component and as part of successor components. The echelon stock formulation permits the derivation of valid inequalities that can be used in an optimal solution method, and facilitates the development of a fast heuristic method for the capacitated problem.