Supply chains provide composite services or products by utilizing autonomous, heterogeneous and/or conversational services provided by independent enterprises. In this paper, we propose a service-oriented process (SOP) model that can model and construct efficient multi-enterprise supply chains as multi-enterprise processes (MEPs). In particular, the SOP model supports service activities for modeling the services themselves, primitives for composing supply chains from services, and primitives for automating service coordination as required by a supply chain. One of the most important aspects of service modeling in SOP is decoupling the service interface from the service implementation. This enables MEPs and the corresponding supply chains to include placeholders, i.e. activities specified only by an abstract interface. These placeholders are substituted at run-time with one of the available services that implement the specified abstract interface. The SOP service selection policy uses a semantic broker that has knowledge about the service capabilities and quality. Therefore, a MEP (and hence its supply chain) is capable of on-the-fly choice of the service providers that are best suited to its objectives (e.g. cheapest, fastest, or just available).