Enterprises of today face the challenge of managing large, complex IT eco-systems consisting of software applications, servers, network routers, and other type of resources. Change management, especially scheduling of changes, is known to be one of the most challenging problems in managing IT operations. In this paper, we propose an optimization model for IT change scheduling that takes into account the constraints and cost factors typically encountered in a service provider environment. In particular, we formulate the model in a way that can be solved using standard mathematical programming techniques (i.e., mixed integer programming). This not only results in strictly optimal solutions, but also provides a scalable means for scheduling a large set of change requests with complex constraints. Furthermore, having a computational efficient optimization solution facilitates the study of the scheduling sensitivity with respect to parameter inaccuracy and leads to more robust change schedules. Finally, we demonstrate the effectiveness of the proposed approach in an IT change management example which is built using insights from a large service delivery account and over two hundred thousand change instances.