Efficient, Effective Lot Sizing for Multistage Production Systems

We consider a multistage, multiproduct production/inventory system in discrete time. When an order is placed for a component it is instantly delivered, and the required amounts of the components consumed in producing the given component are simultaneously withdrawn from their respective inventories. External demand occurs for a single component. We assume that the external demand for the component is nonconstant, deterministic, and must be met without backlogging. We propose two new cluster-based heuristics for this problem. We will show that the first of these heuristics has a worst-case relative cost that is between 1.44 and 2, and the second of these heuristics has a worst-case relative cost of 2. Computational tests indicate that, on the average, these heuristics are within 0.7% and 1.3% of optimal, respectively, and that their performance is very insensitive to the size of the system and to other input parameters.