Lot-sizing for substitutable, production-to-order parts with random functionality yields

A variety of manufacturing processes produce parts that have multiple functionalities or uses, that require different degrees of conformity to standards, and with the degree of conformity of an individual part revealed only after it is produced and inspected. If orders for different product grades need to be met in full but demands are upwardly substitutable, we are faced with a complex multiple-lot-sizing problem. We formulate such a decision model and apply it to some structured numerical examples. The implications of inspections and the computation of their expected costs also are discussed.