THE EFFECT OF QUALITY LOSSES ON BINOMIAL YIELD PROCESSES

Yield losses caused by quality problems can have a significant impact on an overall production process. As a result, planners must consider producing excess output early in the process, so that as losses accumulate, the correct output quantity is obtained. However, as shown here, the problem of determining the starting batch sizes for a multiple-stage production process is significantly complicated when the yield at each operation is random. The model presented in this article can find starting batch sizes for large, complex processes where the yield at each operation is assumed to be a binomial random variable. Equations are developed to find the output distribution of both fabrication (serial) and assembly (parallel) operations. These equations can then be applied sequentially to find the output distribution of a final product that requires any combination of fabrication and assembly operations. The starting batch sizes are then chosen so as to maximize an expected profit function. A marginal improvement heuristic is developed and tested on several numerical examples. In every test case, the marginal improvement heuristic found the optimal solution. Continued research in this area will include attempts to reduce the run time of the marginal improvement heuristic for large target values by including cost considerations in the formulation of the initial heuristic solution. Also, a sensitivity analysis will be conducted to help determine the effects of cost changes and losses on the starting batch sizes. In addition, extensions of this single-period work to a multiple-period scenario will be investigated.