(626c) Optimal Scheduling of Straight Multiproduct Pipelines with Automatic Batch Selection

In the transportation of refined petroleum products by pipeline, the straight pipeline with multiple input and output nodes [1], some of which can be dual-purpose nodes [2-5], is one of the topologies that can be encountered. For this topology, Cafaro and Cerdá [1] first recognized the importance of characterizing the initial status of the pipeline as a collection of old batches (of known products) and empty batches (each comprising a product to be decided by the optimization). Empty batches serve the purpose of allowing the injection of a different product in downstream intermediate input nodes, thus changing the batch/product sequence during the schedule. While it is well-known that the chosen number and location of empty batches affects solution quality, to date, no approach has presented a systematic method of considering all possibilities as part of the optimization.

Mostafaei and Castro [4] presented an efficient continuous-time batch centric formulation for straight pipelines that can handle simultaneous injections and deliveries. The system was divided into segments linking consecutive nodes, with the model allowing for a single batch entering/leaving a segment per time slot. More recently, Liao et al. [5] relaxed this constraint after dividing the system into lines separated by input nodes. It resulted in a reduction in the number of time slots required to find the global optimal solution, a key performance indicator of continuous-time formulations. The practical consequence for decision-making was a decrease in computational time of orders of magnitude. Liao et al. [5] also tested two options for batch numbering. While numbering batches per line avoids the issue of specifying empty batches, because there are no intermediate input nodes in a line, it was found to be a worse option than global batch numbering.

This paper proposes a new mixed-integer formulation for automatically generating the possible initial batch sequences for a given number of batches. It can be viewed as a planning formulation that considers an initial and a final time period. Input nodes and the products initially in the pipeline are viewed as sources whereas output nodes and the final state of the pipeline are viewed as sinks. Sources are then allocated to downstream sinks, by following some logical constraints, to generate an initial batch sequence. The remaining sequences are generated after adding integer cuts that remove previous assignments from the solution space.

Once the sequences are known, we use the mathematical formulation in [5] to generate the respective schedules. Note that several tests are required due to the dependence on the number of batches as well as the number of time slots. Such enumerative solution approach is compared to a simultaneous approach that considers all generated initial sequences in a single optimization run. The comparison also includes a second simultaneous approach that does not require the planning formulation.

Through the solution of a set of benchmark instances of the straight pipeline scheduling problem, we show that the simultaneous approaches have a lower total computational time for the smaller instances. On the other hand, the enumerative approach, by keeping problem size to a minimum, can generate better solutions for the medium to large size instances.

Acknowledgments: Financial support from Fundação para a Ciência e Tecnologia (FCT) through projects CEECIND/00730/2017 and UIDB/04561/2020.

References:

[1] Cafaro DC, Cerdá, J. Optimal scheduling of refined products pipelines with multiple sources. Ind Eng Chem Res. 2009; 48:6675–6689.

[2] Cafaro DC, Cerdá J. Operational scheduling of refined products pipeline networks with simultaneous batch injections. Comput Chem Eng. 2010; 34:1687–1704.

[3] Mostafaei H, Castro PM, Ghaffari-Hadigheh A. Short-term scheduling of multiple source pipelines with simultaneous injections and deliveries. Comput Operat Res. 2016; 73:27–42.

[4] Mostafaei H, Castro, PM. Continuous-time scheduling formulation for straight pipelines. AIChE J. 2017; 63: 1923-1936.

[5] Liao Q, Castro PM, Liang Y, Zhang H. Batch-centric model for scheduling straight multisource pipelines. AIChE J. 2019; 65: e16712.