A Study on Random Yield and Uncertain Demand in Semiconductor Manufacturing

Yield management is important and challengeable in semiconductor industry for the qualitative uncertainty of the final products. The total yield rate of the semiconductor manufacturing process is probabilistic, 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. This paper studies the semiconductor yield management issue of a make-to-stock system with single input, multi-products, multi-demand periods and downward substitution. The whole time horizon of the system operation process can be divided into two stages: the production stage and the allocation stage. In the first stage, the firm invests in raw material before any actual demand is known, and produces multiple types of products with random yield rates. In the second stage, products are classified into different classes by quality, and allocated in numbers of periods. We model the production and allocation problem as a stochastic dynamic program to maximize the profit of the firm. We find three important characteristics of the system: (1) the simple one step upgrade substitution policy is optimal; (2) the objective function is concave in production input; (3) the optimal production input of a related system is nearly identical to that of the dynamic model. We finally design an iterative algorithm to find the optimal production input.