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A reserved delivery subnetwork (RDS) is a semiprivate network infrastructure to enable an information service provider to deliver more consistent service to its customers. In our previous study of the RDS configuration problem, we formulated the problem as a minimum concave cost network flow problem (MCCNFP), and presented an efficient approximation algorithm, largest demand first or LDF, to provide approximate solutions to this NP-hard problem in practice. In this paper, we apply local search algorithms based on negative cost cycle and bicycle reduction to further improve the quality of the results obtained from LDF. Our simulation results show that the local search algorithms improve the quality of LDF solutions, but with added computational complexity. They also further indicate that LDF produces solutions reasonably close to the local optimum without added complexity, and is suitable for large networks in practice.