Pipeline networks are the dominant mode of conveying a wide variety of oil refined products from refineries to distribution terminals. Pipeline infrastructure usually comprises trunk lines serving high-volume, long-haul transportation requirements, and delivering lines moving smaller volumes over shorter distances. Lots of products are mostly sent through trunk lines to bulk terminals, while some portions are branched to delivering lines and supplied to nearby market areas. This work presents a novel continuous-time mixed-integer linear (MILP) formulation for the short-term operational planning of tree-structure pipeline systems. The problem goal is to find the optimal schedule of pumping and delivery operations to satisfy all terminal requirements at minimum operating cost. To this end, model constraints strictly monitor the branching of batches and the creation of new interfaces in delivering lines to avoid forbidden sequences and determine additional reprocessing costs. By allowing the transfer of multiple products to delivering lines during a batch injection, longer runs can be executed, and fewer ones are needed to find the optimal solution. The new approach has been successfully applied to three examples, one of them involving a real-world pipeline network. As compared to previous contributions, significant improvements in both solution quality and CPU time have been obtained.