Economic Lot Size Determination in Multi-Stage Assembly Systems

We consider the optimal lot size problem for multi-stage assembly systems where each facility may have many predecessors but only a single successor. Assumptions include constant continuous final product demand, instantaneous production, and an infinite planning horizon. Costs at each facility consist of a fixed charge per lot and a linear holding cost. Under the constraint that lot sizes remain time invariant, it is proven that the optimal lot size at each facility is an integer multiple of the lot size at the successor facility. This fact is used in the construction of a dynamic programming algorithm for the computation of optimal lot sizes. The algorithm exploits the concept of echelon stock [Clark, A. J., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Management Sci.6 (4, July) 475–490; Clark, A. J., H. Scarf. 1962. Approximate solution to a simple multi-echelon inventory problem. Chapter 5. K. J. Arrow et al., eds. Studies in Applied Probability and Management Science. Stanford University Press, Stanford, California.].