High speed internet and advanced networking technology contribute to having large number of various edge devices in heterogeneous edge-cloud systems. In conventional cloud computing systems, all device data is processed in the centralized cloud servers. The growing number of devices, i.e., increasing amount of device data, poses a challenge to the cloud servers to process data in a time-and energy-efficient manner. Studies show promise to reduce execution time and energy consumption by introducing collaborative edge-cloud computing paradigm. In this work, we study collaborative edge-cloud computing by introducing a framework of pairing the computations at edge and cloud resources to minimize execution time and energy consumption. First, the cloud servers (CSs) are made about 90% utilized by adjusting the device data i.e., computed data. Then, each edge server (ES) is optimized using mathbf{5 0 %} or less of the previously generated device data i.e., cloud computed data. Finally, computations (i.e., device data) are distributed among the ESs and CSs, and performance is assessed to obtain the optimal pairing of computations. A heterogeneous system with one CS, two ESs, 10 edges, and 30 devices of five different types is modeled and simulated using VisualSim. Experimental results show that the proposed method helps reduce execution time and energy consumption by 90% and 56%, respectively. The proposed framework holds a promise for enhancing the scalability of heterogeneous systems, an avenue we intend to explore in our upcoming venture. © 2024 IEEE.