This paper presents a new mixed-integer linear programming (MILP) formulation for the short-term scheduling of liquid transportation by pipeline. It relies on a continuous-time representation featuring a single grid and is suitable for treelike systems with one input node simultaneously feeding multiple output nodes. The novelty is the incorporation of constraints for rigorously enforcing forbidden product sequences and ensuring a single batch inside idle segments. We tackle a real-life problem from the Iranian pipeline network, generating an optimal schedule that increases pipeline capacity by 6.2%, meeting demand from the weekly plan, fourteen hours earlier. We also solve three benchmark problems from the literature. The results show a significantly better performance than a closely related, state-of-the-art, product-centric formulation, which is unable to find a feasible solution for a problem that can now be solved to proven global optimality. It is primarily because multiple batches can enter/leave segments during a time slot.