Biopharmaceuticals represent the fastest growing sector of the global pharmaceutical industry. Cost-efficient production of these biologic drugs requires a robust host organism for generating high titers of protein during fermentation. Understanding key cellular processes that limit protein production and secretion is, therefore, essential for rational strain engineering. Here, with single-cell resolution, we systematically analysed the productivity of a series of Pichia pastoris strains that produce different proteins both constitutively and inducibly. We characterized each strain by qPCR, RT-qPCR, microengraving, and imaging cytometry. We then developed a simple mathematical model describing the flux of folded protein through the ER. This combination of single-cell measurements and computational modelling shows that protein trafficking through the secretory machinery is often the rate-limiting step in single-cell production, and strategies to enhance the overall capacity of protein secretion within hosts for the production of heterologous proteins may improve productivity.