Simultaneous optimization of decisions using a linear utility function

The purpose of this article is to simultaneously optimize decision rules for combinations of elementary decisions. With this approach, rules are found that make more efficient use of the data than could be achieved by optimizing these decisions separately. The framework for the approach is derived from Bayesian decision theory. To illustrate the approach, two elementary decisions (selection and mastery decisions) are combined into a simple decision network. A linear utility structure is assumed. Decision rules are derived both for quota-free and quota-restricted selection-mastery decisions in case of several subpopulations. An empirical example of instructional decision making in an individual study system concludes the article.