In advanced service oriented systems, complex applications, described as abstract business processes, can be executed by invoking a number of available Web services. End users can specify different preferences and constraints and service selection can be performed dynamically identifying the best set of services available at runtime. In this paper, we introduce a new modeling approach to the Web service selection problem that is particularly effective for large processes and when QoS constraints are severe. In the model, the Web service selection problem is formalized as a mixed integer linear programming problem, loops peeling is adopted in the optimization, and constraints posed by stateful Web services are considered. Moreover, negotiation techniques are exploited to identify a feasible solution of the problem, if one does not exist. Experimental results compare our method with other solutions proposed in the literature and demonstrate the effectiveness of our approach toward the identification of an optimal solution to the QoS constrained Web service selection problem. Index Terms—Web services, quality of service, service composition, integer programming.