Recent work has suggest plant level heterogeneity and discrete production processes can produce problems for estimation. A structural model of discrete production decisions by heterogeneous plants is constructed and as a case study. estimated for the US Portland cement industry. In particular, an ordered pro bit model is extended to encapsulate the structural model and to handle incomplete ordering. This is the first application of the ordered pro bit model for the direct estimation of a short run cost junction. The results broadly support the structure suggested by the industry technology and competitive conditions. Differences between industry averages of input requirements and many of the estimates of these coefficients are statistically insignificant.