Coordinating a two-level supply chain with production interruptions to restore process quality

The classical inventory model, known as the lot size problem (LSP), assumes items produced and stocked to be of perfect quality. In reality, production processes are not defect free. Such imperfect processes generate defects that are reworked, and in some cases scrapped. The move by practitioners towards smaller lot sizes; e.g., just-in-time (JIT), as a mean of improving process and product quality prompted researchers to modify the LSP to represent reality more faithfully. The studies conducted by these researchers confirmed the observed benefits of smaller lot sizes. The inventory models developed in these studies assume that defects increase as the lot size increases, and that adjusting the process within a production cycle is not possible. Contrary to this assumption, in a JIT environment workers are authorized to stop production if a quality or production problem arises. This practice encouraged Khouja [Khouja, M. (2005). The use of minor setups within production cycles to improve product quality and yield. International Transactions in Operations Research, 12(4), 403–416] to reformulate some inventory models which take into account the negative relationship between lot size and quality and the possibility of performing minor setups. This requires stopping the process during a production cycle. This paper investigates the work of Khouja in a centralized decision model where players in a two-level (manufacturer–retailer) supply chain coordinate their orders to minimize their local costs and that of the chain. Mathematical models are developed with numerical results discussed.