A Fast, Network-based, Hybrid Heuristic for the Assignment of Students to Schools

In an era of declining and fluctuating enrolments, the determination of appropriate school sizes and student assignments poses difficult problems for administrators. For two decades, researchers have worked with variants of a linear programming districting model which minimizes total weighted distance as all students are assigned to schools constrained by both capacity and racial balance limitations. This model could aid in the generation of districting alternatives, but is difficult to solve in realistic applications with generalized solution procedures because of overall problem size. This has prompted the development of fast, network-based models, solvable with special algorithms and codes. We show, however, that these approaches all contain major shortcomings. We present a fast, hybrid heuristic based upon two network representations. Computational results demonstrate this to be a very fast solution approach for the general case of this districting problem.