A joint design of rectifying inspection plans and service capacities for multi-products

In this paper, we study a joint design problem of sampling inspections and service capacities for multi-products. Products are supplied in batches after rectifying inspections, that is, rejected lots are 100% inspected and defective products are reworked to good ones. When supplied, all defective products are uncovered through total inspection and returned to service. By exploiting the first and second order properties of the objective function, we identify the optimal inspection policies and service capacities for individual products, and develop allocation algorithms to obtain an optimal allocation of the limited total service capacity to products with the small number of computations.