Detailed Scheduling of Single-Source Pipelines with Simultaneous Deliveries to Multiple Offtake Stations

Continuous formulations for the scheduling of single-source refined-product pipelines with multiple distribution terminals have already been published. They help the scheduler make key operating decisions such as the sequence of batch injections at the input station, the batch sizes, the start and end times of pumping runs, and the set of aggregate product deliveries to perform during each run. In this way, the aggregate pipeline schedule is defined. However, the scheduler has yet to decide not only on the order of execution of such product extractions but also the number of batch cuts to make to accomplish each aggregate delivery. Therefore, it becomes necessary to refine the aggregate schedule. Most previous contributions providing a refined delivery plan have assumed that product withdrawals at receiving locations over a single-source pipeline should be made one at a time. However, such pipelines do not actually work in this way because their operators usually perform simultaneous product deliveries to cut down on pump operating and maintenance costs. By doing so, they seek to reduce the number of pipeline segments where the liquid flow should be restarted. This article presents a new mixed-integer linear programming (MILP) continuous formulation for developing the detailed schedules of single-source pipelines assuming that simultaneous deliveries to multiple receiving terminals can be performed. The problem goal is to minimize the overall flow restart and stoppage volumes through the smallest number of pipeline operations. Solutions to two examples obtained with the proposed approach present significant reductions in both the operating cost and the CPU time with respect to previous contributions.