Continuous-time scheduling models for multiproduct pipelines typically view the contents of a pipeline as a set of batches. It facilitates tracking batch coordinates but prevents rigorously enforcing forbidden product sequences when dealing with intermediate dual-purpose nodes. Such models require the initial characterization of the pipeline and total number of batches as inputs, decisions that can be non-trivial. To overcome these limitations, this paper presents a new mixed-integer linear programming (MILP) formulation for straight pipelines with a single tuning parameter, the number of event points in the grid. It is derived from Generalized Disjunctive Programming (GDP) followed by a convex hull reformulation. Compared to a product-centric formulation based on the Resource-Task Network (RTN), it is much simpler, smaller in size and can be up to two orders of magnitude faster. Comparison to its batch-centric counterpart is not as favorable, the highlight being an 8% improvement in makespan for a benchmark problem.