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The resource allocation in cloud computing determines the allocation of computer and network resources of service providers to service requests of users for meeting user service requirements. It is not scalable to solve the resource allocation problem as an optimization problem to obtain the optimal solution in real time. This paper presents the development and testing of heuristics for the efficient resource allocation to obtain near-optimal solutions in a scalable manner. We first define the resource allocation problem as a Mixed Integer rogramming (MIP) optimization problem and obtain the optimal solutions for various resource-service problem types. Based on the analysis of the optimal solutions, we design heuristics for the efficient resource allocation. Then we evaluate the performance of the resource allocation heuristics using various resource-service problem types and different numbers of service requests and resources. The results show the comparable performance of the heuristics to the optimal solutions. The resource allocation heuristics also demonstrate the better computational efficiency and thus scalability than solving the MIP problems to obtain the optimal solutions. Keywords: Resource allocation; Clouds computing; Heuristics; Mixed integer programming