Nowadays, the data centers have become a significant physical infrastructure for the purpose of supporting various Internet applications like cloud services, entertainment, web search and social networking. The traffic among the data centers is growing rapidly accompanied by the services that are obtained. The data centers are connected via fiber channels to support long-haul networks and high data rate transmissions by utilizing various modulation techniques. However, it has some drawbacks such as increased delay, computational complexities, high wavelength consumption, link failures, etc. Recently, researchers are focusing on improving the survivability and wavelength usage efficiency in optical data center networks. In this work, a novel framework depending on the concept of content connectivity is proposed for optical data center networks. Here, a mixed integer linear programming (MILP) is utilized for transmitting the data through optical data centers. The main intention of this research is to improve the performance and wavelength efficiency in optical data center networks. The performance of the MILP approach is evaluated and compared with the existing integer linear programming (ILP) technique and found that this new approach provides better performance with higher wavelength efficiency and reduced wavelength consumption.