(708c) Novel Discrete-Time MILP Scheduling Model for Pipeline Systems

Pipelines are widely referred as the fifth transportation mode, being extensively used to safely transport crude oil and its derivatives over complex networks. They are often multiproduct systems and can operate continuously day and night. The flexibility of pipelines for the transportation of multiple products, coupled with multiple system configurations, has attracted the interest of several research groups to the pipeline scheduling problem (PSP). Scheduling of dispatching refined petroleum products through the multi-product pipeline involves several decisions, such as planning the optimal sequence of products inside the pipeline, determining the length and starting time of each pumping run, together with the optimal timing of delivery to receiving terminals so as to meet product demands with minimum delay. Operational constraints include: flow rate limitations, forbidden sequences, filler batch and inventory constraints. Different types of rigorous optimization approaches have been proposed to study the PSP, with most of them consisting of solving a discrete- or continuous-time mixed integer linear programming (MILP) formulation. Discrete-time approaches divide the scheduling horizon into time intervals of fixed duration and the pipeline into packages of uniform sizes, each containing a single product [1-2], whereas continuous-time representations consider the length of time slots as continuous variables to be selected by the optimization [3-4].

The large majority of contributions to the PSP have adopted a continuous-time representation to model product movements inside the pipeline. In practice, however, they often lead to suboptimal solutions for two reasons: (i) poor LP relaxation due to the presence of inefficient big-M constraints and (ii) the minimum number of time slots required to represent the optimal solution is unknown. To this end, this work develops a discrete-time MILP model for the scheduling of a straight pipeline with a single refinery and multiple depots. Compared to other discrete-time formulations, the proposed approach does not need to divide pipeline segments into packs of equal sizes and allows a pumping operation to span over multiple time slots, thus leading to better solutions and fewer number of ON/OFF pump switching operations. To ensure an efficient model by design, we rely on Generalized Disjunctive Programming (GDP) [5-6] and develop disjunctions that mostly allow for a compact convex hull reformulation. The proposed approach is illustrated by solving two case studies from the literature. Results show that the approach is applicable for real case problems.

Acknowledgments: Hossein Mostafaei and Iiro Harjunkoski fully appreciate financial support from Academy of Finland project “SINGPRO”, Decision No. 313466. Pedro Castro acknowledges support from Fundação para a Ciência e Tecnologia through UID/MAT/04561/2019.

References:

[1] Rejowski, R., Pinto, J.M., 2003. Scheduling of a multiproduct pipeline system. Comput. Chem. Eng. 27, 1229–1246.

[2] Herrán, A., de la Cruz, J. M., de Andrés, B., 2010. Mathematical model for planning transportation of multiple petroleum products in a multi-pipeline system. Comput. Chem. Eng. 34, 401-413.

[3] Cafaro, D.C., Cerdá, J., 2004. Optimal scheduling of multiproduct pipeline systems using a non-discrete MILP formulation. Comput. Chem. Eng. 28, 2053-2068.

[4] Ghaffari-Hadigheh, A., Mostafaei H. (2015). On the scheduling of real world multiproduct pipelines with simultaneous delivery. Optimization and Engineering, 16, 571-604.

[5] Balas, E., 1979. Disjunctive programming. Annals of Discrete Mathematics 5, 3-51.

[6] 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.