Allocation of Chips to Wafers in a Production Problem of Semiconductor Kits

The problem of maximizing the production of good sets of semiconductor chips under random yield is reexamined in this paper. (A set of semiconductor chips is called a semiconductor kit.) This problem has been considered by Avram and Wein (Avram, F., L. Wein. 1992. A product design problem in semiconductor manufacturing. Opns. Res.40(5) 986–998.) and Singh et al. (Singh, M. R., C. T. Abraham, R. Akella. 1988. Planning for production of a set of components when yield is random. Fifth IEEE CHMT Internat. Electronic Manufacturing Technology Proc.). To solve this problem we show that under certain combinations of assumptions the production process can be replaced by a black box. The use of the black box model considerably simplifies the analysis and reduces the simulation effort required for carrying out parametric analysis of the proposed solution procedure. The model includes that of Avram and Wein, and we extend their results to more general settings and strengthen their conclusions. Using the black box model, it is shown that the strategy of placing different types of chips on a single wafer gives larger yield of kits in a stochastic sense than the traditional method of placing single types of chips on a wafer. We compare the production of kits under different chip design and lot release policies and also carry out a parametric analysis with respect to factors such as set proportions and yield.