Optimizing the spatial assignment of schools through a random mechanism towards equal educational opportunity: A resemblance approach

Although it is generally agreed that public primary education should be equally available to all, a spatial disparity of educational opportunity exists worldwide, for wealthy families can acquire residential locations with better access to the best schools. Random allocation of school places is considered to be an effective approach for breaking such spatial linkages. This study addresses the problem of achieving the optimal spatial equality of educational opportunity by re-assigning school places to demand nodes using a combined mechanism that introduces a random allocation into a proximity-based system. This study proposes the use of a probability distribution for a full description of educational opportunity. A new spatial allocation optimization model towards equal educational opportunity with the maximum school travel distance constraints and capacities constraints was developed to maximize the resemblance between the probability distributions across demand nodes (RES-based model). This model was applied to a case study of primary school allocation in the Shijingshan District of Beijing, China, and was resolved in a heuristic way. The solution was compared with those provided by a capacitated proximity-based model and a model also using the random mechanism but measuring educational opportunity by expectation values (VAR-based model). It was found that the introducing of random mechanism could significantly improve the spatial equality of educational opportunity with a significant loss of spatial efficiency. In addition, the solution provided by the RES-based model was quite different to that provided by the VAR-based model. An improvement in the resemblance of demand node probability distributions might lead to an increase in the variance of expectations. The resemblance approach proposed in this study may also be applied to the optimization of other random objectives.