The appropriate deployment of web service operations at the service provider site plays a critical role in the efficient provision of services to clients. In this paper, we assume that a service provider has several servers over which web service operations can be deployed. Then, given a workflow of web services and the topology of the servers, the most efficient mopping of operations to servers must be discovered. Efficiency is measured in terms of two cost functions that concern the execution time of the workflow and the fairness of the load distribution among the servers. We study different topologies for the workflow structure and the server connectivity and propose a suite of greedy algorithms for each combination.