Supplier development in a two-level lot sizing problem with non-conforming items and learning

Companies have to account for continuously evolving technologies that are driven by the consumer's appetite for new and innovative products, requiring them to modify their production systems to become flexible, where items do not have standard features and specifications. It is normal though that new products and processes would result in a considerable proportion of non-conforming items produced by the supplier and rejected by the buyer (a company). We consider a two-level joint production system that investigates the behavior of the supplier and the buyer's production systems. We assume that the proportion of non-conforming items produced by the supplier is a random variable whose mean and variance reduce due to learning effects. We examine investing in the supplier's process to speed up the learning process and propose a mathematical framework to quantify the effectiveness of an investment. Heuristics are developed to solve those mathematical models. We consider in this paper a finite planning horizon since products, today, have short lives, and we present a numerical study to show that the proposed action can be economically beneficial to the system.