Design of sampling inspections and service capacities for multi-products

In this paper, we study the joint design of sampling inspections and service capacities for multi-products. Products of different defect rates which are either deterministic or random variables are supplied in batches after sampling inspection and rework. When supplied, all defective products that have not been inspected in batches are uncovered through total inspection and returned to service. We identify the optimal inspection policies and service capacities for multi-products reflecting the relationships between inspection rework costs and service provision costs. We also develop a marginal allocation algorithm for the optimal allocation of the limited total service capacity to products as well as inspection quantities.