A consignment stock is a type of supply-chain coordination for the management of supply-chains in which there is a joint vendor and buyer policy that is mainly focused on having the vendor manage the buyer's inventory. This thesis aims to investigate the consignment stock strategy in a single-vendor single-buyer supply-chain context considering imperfect items that may be produced from an imperfect production process. It develops a flexible mathematical model that allows for managerial decisions with regards to imperfect items and seeks to minimize costs (maximize profits) of the supply-chain. Such managerial decisions include scrapping items at a cost, selling them for a marginal profit to a secondary market, applying re-work, and/or applying minor setups to restore the production process. Results show that the introduction of imperfect items increases the batch size and reduces the number of shipments. Minor setups were shown to reduce cost, increase the number of shipments and reduce its size.