Input to the Load Balanced Demand Distribution (LBDD) consists of the following: (a) a set of public service centers (e.g., schools); (b) a set of demand (people) units and; (c) a cost matrix containing the cost of assignment for all demand unit-service center pairs. In addition, each service center is also associated with a notion of capacity and a penalty which is incurred if it gets overloaded. Given the input, the LBDD problem determines a mapping from the set of demand units to the set of service centers. The objective is to determine a mapping that minimizes the sum of the following two terms: (i) the total assignment cost between demand units and their allotted service centers and, (ii) total of penalties incurred. The problem of LBDD finds its application in the domain of urban planning. An instance of the LBDD problem can be reduced to an instance of the min-cost bi-partite matching problem. However, this approach cannot scale up to the real world large problem instances. The current state of the art related to LBDD makes simplifying assumptions such as infinite capacity or total capacity being equal to the total demand. This paper proposes a novel allotment subspace re-adjustment based approach (ASRAL) for the LBDD problem. We analyze ASRAL theoretically and present its asymptotic time complexity. We also evaluate ASRAL experimentally on large problem instances and compare with alternative approaches. Our results indicate that ASRAL is able to scale-up while maintaining significantly better solution quality over the alternative approaches. In addition, we also extend ASRAL to para-ASRAL which uses the GPU and CPU cores to speed-up the execution while maintaining the same solution quality as ASRAL.