This paper presents a simplex algorithm for finding a nonnegative solution (or demonstrating the inconsistency) of y = a + Ax where A is positive semi-definite. Linear and quadratic programming problems are of this form. The function exhibited in the proof of finiteness does not appear in other algorithms. If a primal feasible solution is available in the linear programming case, the actual choice of pivot rows is exactly that made in the usual lexicographic simplex method.
Since 1981 the University of Chicago Graduate School of Business (GSB) has used a computerized course registration system that allocates limited classroom and faculty resources while satisfying students' preferences among course offerings. The method a) uses a market approach (complete with clearing prices) for allocating course sections to students, b) allows students to express preferences for combinations of courses rather than for single courses, c) allows students to express preferences for courses over multiple school terms rather than just one, and d) requires no waiting in registration queues.
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