Computational Grids, coupling geographically distributed resources such as PCs, workstations, clusters, and scientific instruments, have emerged as a next generation computing platform for solving large-scale problems in science, engineering, and commerce. However, application development, resource management, and scheduling in these environments continue to be a complex undertaking. In this article, we discuss our efforts in developing a resource management system for scheduling computations on resources distributed across the world with varying quality of service. Our service-oriented grid computing system called Nimrod-G manages all operations associated with remote execution including resource discovery, trading, scheduling based on economic principles and a user defined quality of service requirement. The Nimrod-G resource broker is implemented by leveraging existing technologies such as Globus, and provides new services that are essential for constructing industrial-strength Grids. We discuss results of preliminary experiments on scheduling some parametric computations using the Nimrod-G resource broker on a world-wide grid testbed that spans five continents.