This document proposes a new Ranking Chaos Optimization (RCO) algorithm to solve the dual scheduling problem of cloud services and computing resources (DS-CSCR) in private clouds. It introduces the DS-CSCR concept and models the characteristics of cloud services and computing resources. The RCO algorithm uses ranking selection, individual chaos, and dynamic heuristic operators. Experimental results show RCO has better searching ability, time complexity, and stability compared to other algorithms for solving DS-CSCR. Future work is needed to study additional quality of service properties and improve RCO for other optimization problems.