Location-based services provide opportunities to organizations for tracking and utilizing their resources. Moreover, some corporations prefer to outsource their database management services. In the literature, privacy preservation techniques in outsourced spatial databases for several query types, such as nearest neighbor, K-nearest neighbor, and proximity search, have been examined. In this paper, we present an efficient application of the capacity and coverage-constrained assignment query on outsourced spatial databases. In the proposed technique, we introduce a novel spatial transformation strategy (square spiral encoding) to achieve privacy efficiently for approximate assignment query results. To process the assignment query, we use the parallel auction algorithm. We implemented and tested the assignment query with the proposed technique for correctness and efficiency.