Simultaneous optimization of decisions using a linear utility function

The purpose of this paper is to simultaneously optimize decision rules for combinations of elementary decisions. As a result of this approach, rules are found that make more efficient use of the data than does optimizing those decisions separately. The framework for the approach is derived from empirical Bayesian 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 for several subpopulations. An empirical example of instructional decision making in an individual study system concludes the paper. The example involves 43 freshmen medical students (27 were disadvantaged and 16 were advantaged with respect to elementary medical knowledge). Both the selection and mastery tests consisted of 17 free-response items on elementary medical knowledge with test scores ranging from 0 to 100. The treatment consisted of a computer-aided instructional program.