A stochastic dynamic programming approach-based yield management with substitution and uncertainty in semiconductor manufacturing

Yield management is important and challengeable in semiconductor industry for the quality uncertainty of the final products. The total yield rate of the semiconductor manufacturing process is uncertain, each product is graded into one of several quality levels according to performance before being shipped. A product originally targeted to satisfy the demand of one product may be used to satisfy the demand of other products when it conforms to their specifications. At the same time, the products depreciate in allocation periods, which mainly results from technical progresses. This paper studies the semiconductor yield management issue of a make-to-stock system with single input, multi-products, multi-demand periods, upward substitution and periodic depreciation. The whole time horizon of the system operation process can be divided into two stages: the production stage and the allocation stage. At the first stage, the firm invests in raw materials before any actual demand is known and produces multiple types of products with random yield rates. At the second stage, products are classified into different classes by quality and allocated in numbers of periods. The production and allocation problem are modeled as a stochastic dynamic program in which the objective is to maximize the profit of the firm. We show that the PRA (parallel allocation first, then upgrade) allocation policy is the optimal allocation policy and the objective function is concave in production input. An iterative algorithm is designed to find the optimal production input and numerical experiments are used to illustrate its effectiveness.