(715f) Continuous-Time Scheduling Formulation for Pipeline Systems with Branches
Research on pipeline scheduling can be divided into product- [1-4] and batch-centric approaches [5-9]. The latter, convert product into batches when entering the pipeline, admitting two or more batches of a product inside a pipeline segment. Because multiple batches can enter/leave a segment during a slot , their other advantage is fewer time slots to represent a schedule. There are however, three disadvantages: (i) the way in which batch coordinates are computed makes the extension to generic systems with reversible flow quite difficult; (ii) there are more tuning parameters affecting solution quality, unless there is a single input node; (iii) constrains for enforcing forbidden sequences (very common in practice) are not rigorous, since they refer to the injected batch sequence, which can be altered by removing the batch at an intermediate output node or a branch (different path taken).
In this work, we extend our modular batch-centric continuous-time formulation, from straight pipelines  to treelike systems with a single input node and multilevel branching (our work in  features a more complex mixed-integer linear programming model and is only suitable for one-level branching). We also propose rigorous constraints for handling forbidden product sequences that are derived from Generalized Disjunctive Programming [11-13].
The proposed MILP model is used to tackle a real-life problem from the Iranian Oil Pipelines and Telecommunication Company (IOPTC), addressing, for the first time, the preference for schedules with a single product inside idle segments. The problem involves the first-week-of-November-2017 plan for transporting gasoline, kerosene and gasoil from the refinery in Tabriz to the cities of Maragheh, Miandoab and Urmia.
The rule-based schedule implemented by the company failed to deliver the full product demand, whereas our optimization model could do it more than half a day earlier, increasing pipeline capacity by 6.2%. When considering 3 benchmark problems from the literature, we were able to obtain new best schedules for all, due to a superior computational performance. In particular, when compared to the most general (product-centric) formulation from the literature  in terms of system configuration and directions of flow, we could prove global optimality for the problem with the highest number of segments, whereas the model in  could not even find a feasible solution.
Acknowledgments: Financial support from FundaÃ§Ã£o para a CiÃªncia e Tecnologia (FCT) through projects IF/00781/2013 andUID/MAT/04561/2013.
 Rejowski, R., Pinto, J.M., 2003. Scheduling of a multiproduct pipeline system. Comput. Chem. Eng. 27, 1229â1246.
 MagatÃ£o, L., Arruda, L.V.R., Neves, F.A., 2004. A mixed integer programming approach for scheduling commodities in a pipeline. Comput. Chem. Eng., 28, 171-185.
 Castro, P.M., 2010. Optimal scheduling of pipeline systems with a resource-task network continuous-time formulation. Ind. Eng. Chem. Res.49, 11491-11505.
 Castro, P.M., Mostafaei, H., 2017. Product-centric continuous-time formulation for pipeline scheduling. Comp. Chem. Eng. 104, 283-295.
 Cafaro, D.C., CerdÃ¡, J., 2004. Optimal scheduling of multiproduct pipeline systems using a non-discrete MILP formulation. Comput. Chem. Eng. 28, 2053-2068.
 Relvas, S., Matos, H.M., Barbosa-PÃ³voa, A.P.F.D., Fialho, J., Pinheiro, A.S., 2006. Pipeline scheduling and inventory management of a multiproduct distribution oil system. Ind. Eng. Chem. Res. 45, 7841â7855.
 MirHassani, S.A., Jahromi, H.F., 2011. Scheduling multi-product tree-structure pipelines. Comput. Chem. Eng. 35, 165â176.
 Mostafaei, H., Ghaffari-Hadigheh, A., 2014. A General modeling framework for the long-term scheduling of multiproduct pipelines with delivery constraints. Ind. Eng. Chem. Res. 53, 7029-7042.
 Mostafaei, H., Castro, P.M., 2017. Continuous-time scheduling formulations for straight pipelines. AIChE J. 63, 1923-1936.
 Mostafaei, H., Castro, P.M., Ghaffari-Hadigheh, A., 2015. Novel monolithic MILP framework for lot-sizing and scheduling of multiproduct treelike pipeline networks, Ind. Eng. Chem. Res. 54, 9202-9221.
 Balas, E., 1979. Disjunctive programming. Annals of Discrete Mathematics 5, 3-51.
 Raman, R., Grossmann, I.E., 1994. Modeling and computational techniques for logic based integer programming. Comput. Chem. Eng. 18, 563-578.
 Castro, P.M., Grossmann, I.E., 2012. Generalized disjunctive programming as a systematic modeling framework to derive scheduling formulations. Ind. Eng. Chem. Res. 51, 5781-5792.
 Castro, P.M., 2017. Optimal scheduling of multiproduct pipelines in networks with reversible flow. Ind. Eng. Chem. Res. 56, 9638-9656.