The House of Quality has been widely discussed as a mechanism for converting customer attributes into engineering characteristics to ensure the designqualityof new products and processes. In the past, this process has been subjective and heuristic. In this paper, we present a mathematical programming model for determining the optimal settings for engineering characteristics based on value functions constructedtocapture customer preferences. The model can be used with either traditional subjective measures of customer preference or incorporate empirical models based on quantitative data. The robustness of the optimal solution to randomness in parameter estimates is investigated. An example is used to demonstrate the procedure.