Despite the increasing use of mobile computing, exploiting its full potential is difficult due to its inherent characteristics such as error-prone transmission channels, diverse node capabilities, frequent disconnections and mobility. Mobile Cloud Computing (MCC) is a paradigm that is aimed at overcoming previous problems through integrating mobile devices with cloud computing. Mobile devices, in the traditional client-server architecture of MCC, offload their tasks to the cloud to utilize the computation and storage resources of data centers. However, along with the development of hardware and software technologies in mobile devices, researchers have begun to take into consideration local resource sharing among mobile devices themselves. This is defined as the cooperation based architecture of MCC. Analogous to the conventional terminology, the resource platforms that are comprised of surrounding surrogate mobile devices are called local resource clouds. Some researchers have recently verified the feasibility and benefits of this strategy. However, existing work has neglected an important issue with this approach, i.e., how to construct local resource clouds in dynamic mobile wireless networks. This paper presents the concept and design of a local resource cloud that is both energy and time efficient. Along with theoretical models and formal definitions of problems, an efficient heuristic algorithm with low computational complexity is also presented. The results from simulations demonstrate the effectiveness of the proposed models and method.