In this paper, we first present a linear programming based approach for modeling and solving the resource matching problem in grid environments with heterogeneous resources. The resource matching problem described takes into account resource sharing, job priorities, dependencies on multiple resource types, and resource specific policies. We then propose Web service style architecture for online matching of independent jobs with resources in a grid environment and describe a prototype implementation. Our preliminary performance results indicate that the linear programming based approach for resource matching is efficient in speed and accuracy and can keep up with high job arrival rates of an important criterion for online resource matching systems. Also, the Web service style architecture makes the system scalable and extendable. It can also be integrated with other existing grid services in a straightforward manner.