Undoubtedly, the customer service is a central aspect in supply chain management and it is clear that all supply chain partners actively participate in its fulfillment at certain degree. However, the control of service could be more concentrated in some supply chain actors or functional areas in the chain. In certain chains, it is well recognized the dominance exercised by suppliers, manufacturers, distributors, retailers or even the customers. This dominance may be induced by resource limitations or bottlenecks, by power influences within the chain or by other factors. Considering that, in real supply chain systems, either production or distribution could dominate the service fulfillment, we present in this article a review which explores how the dominance in service in supply chain mathematical programming models has been considered. A novel taxonomy is proposed and it includes bottlenecks identification, shortages traceability, dominance perceived in the solution strategy, the marginal post-optimal analysis or use of shadow prices, among others.