(733a) Optimal Scheduling of Multiproduct Liquid Pipelines with Reversible Flow

The problem of scheduling multiproduct liquid pipelines has received considerable attention over the last 15 years [1-2]. Different mathematical formulations have been proposed featuring alternative ways to handle time and to keep track of batch/product coordinates inside the pipeline. Other items used for classification regard the structure of the pipeline (e.g. straight, tree-like, mesh) and the flow direction, unidirectional in most cases with a couple of articles allowing for reversible flow [3-4].

The main goal of pipeline operators is to meet demand on time. The pipeline scheduling problem should thus include the inventory management problem of the tanks linked to the pipeline nodes, to avoid running on empty or exceeding the maximum storage capacity. Besides the interaction with the pipeline, tanks can receive inputs from refineries (assumed in this work to occur at a constant rate) and send products to local markets. The delivery rate shouldn’t exceed a maximum value that is typically lower than maximum incoming flowrate from the pipeline. It is thus important not to leave all market deliveries to the last moment.

Following up on recent work [5-6], this paper presents a new continuous-time formulation for scheduling multiproduct pipelines with incompressible fluids. It is modular, in the sense that it views a pipeline system as a collection of nodes and segments, allowing it to tackle any structural configuration. Furthermore, it allows for flow reversals as many times and in as many segments as required. Nodes can be of different types ranging from junction nodes with no storage, to intermediate dual purpose nodes with storage tanks linked to refineries and local markets. The proposed mixed-integer linear programming formulation (MILP) does not explicitly divide the products into batches and features a single tuning parameter, the number of event points in the single time grid [6]. It has been derived from Generalized Disjunctive Programming [7-9] following a convex hull reformulation [10] of all the constraints inside the disjunctions to obtain a computationally efficient formulation by design.

The performance of the new formulation is illustrated on a set of six benchmark problems from the literature. Three involve straight pipelines with reversible flow [4,11], two feature tree-like systems with unidirectional flow [12] and the last, a mesh structure with single flow direction [13]. The results show a 5 to 10% reduction in makespan for 4 example problems.

Nevertheless, for one of the reversible flow problems (with 9 products), we got a 30% worse solution in the allocated computational time, indicating that the constraint of a single leaving product per time slot in a segment should be relaxed in terminal nodes, to decrease the number of event points required to represent the schedule, which is well-known to have a major impact in computational performance.

For the mesh-structure problem, the makespan obtained was also 8.5% worse than the best reported [13]. However, after careful examining the solution in [13], we realized that minimum segment flowrate constraints and the maximum flowrate delivery constraints to local markets were not being met. It shows that our formulation is more rigorous at tackling the simultaneous pipeline scheduling and inventory control problem.

Acknowledgments: Financial support from Fundação para a Ciência e Tecnologia (FCT) through projects IF/00781/2013 and UID/MAT/04561/2013.

References:

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