The impact of quality considerations on material flow in two-stage inventory systems

Supply chain management literature calls for coordination between the different members of the chain. Inventory models achieve this coordination along a supply chain by making the lot size at an upstream entity an integer multiplier of the lot size at the adjacent downstream entity. Such models assume that all components produced are of acceptable quality and may cause suppliers to produce larger quantities than what is optimal. In this paper, we formulate and solve two-stage supply chain inventory models in which the proportion of defective products increases with increased production lot sizes. We show that quality considerations can lead to significant reduction in production lot sizes. In addition, the models show that most benefits to the supply chain are attained from the suppliers producing on a just-in-time basis rather than delivering to their customers just-in-time. We derive closed-form expressions for the optimal lot sizes for a two-stage supply chain under deterministic and then stochastic demand and illustrate the models with numerical examples.