464173 Scheduling Straight Multiproduct Pipelines with Generalized Disjunctive Programming

Thursday, November 17, 2016: 12:49 PM
Carmel I (Hotel Nikko San Francisco)
Hossein Mostafaei, Department of Applied Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran (Islamic Republic of) and Pedro M. Castro, CMAFCIO, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal

Pipelines are the most cost-effective way of transporting large quantities of refined petroleum products (e.g. gasoline, kerosene, jet fuel, diesel, heating oil, liquefied petroleum gases) over large distances. Pipelines have grown considerably and have become structurally more complex. The main challenge of pipeline scheduling is to ensure that oil products form refineries arrive to the distribution centers serving local markets at the right time and preferably at the lowest cost. It involves batch sizing, sequencing and respecting minimum and maximum flowrate limits on the different segments that make the pipeline.

Pipeline scheduling models are typically of the mixed-integer linear type (MILP) unless an accurate representation of the pumping cost is required [1] that transforms the problem into a mixed-integer nonlinear program (MINLP). Similarly to general scheduling formulations, one may rely on a discrete or continuous representation, which in this case applies to both time and volume inside the pipeline. In this paper, we present a full-space continuous-time and volume formulation for straight pipelines that uses a single time grid to keep track of events taking place. The straight pipeline includes multiple intermediate nodes in addition to the first refinery and the last depot. The nodes can be single purpose (either input or output) or dual purpose nodes that ship and receive materials at different times.

We follow up on our recent work in [2] dealing with simultaneous injections and deliveries. The novelty is that we now allow for interacting pumping runs, where an intermediate refinery node can feed the downstream segment simultaneously with the upstream node, provided that the same product is involved. It allows to reduce the makespan as well as the number of time slots required to transfer the petroleum products and meet demand. Since the latter affects most model variables and constraints, the computational performance is also improved. Real-world case studies involving an Iranian pipeline are used to illustrate the advantages of the proposed model.

To ensure an efficient model by design, we rely on Generalized Disjunctive Programming (GDP) [3-5] and develop disjunctions that mostly allow for a compact convex hull reformulation [4]. Disjunctions relate binary and continuous variables, whereas the majority of constraints relating continuous variables are essentially mass balances. Finally, the logic propositions relate the different sets of binary variables. As such, a simpler and more systematic model is derived compared to our recent GDP efforts for pipeline scheduling [2, 6] (where a few constraints were developed ad-hoc), potentially making it easier to generalize to tree-like structures.

Acknowledgments: Financial support from Iranian Ministry of Science, Research and Technology and Fundação para a Ciência e Tecnologia (FCT) through the Investigador FCT 2013 program and project UID/MAT/04561/2013.

References:

[1] V.G. Cafaro, D.C. Cafaro, C.A. Mendéz, J. Cerdá, MINLP model for the detailed scheduling of refined products pipelines with flow rate dependent pumping costs, Comput Chem Eng 72 (2014) 210–221.

[2] H.Mostafaei, P.M. Castro, A. Ghaffari-Hadigheh, Short-term scheduling of multiple source pipelines with simultaneous injections and deliveries, Comput Oper Res 73 (2016) 27-42.

[3] R. Raman, I.E. Grossmann, Modeling and computational techniques for logic based integer programming, Comput Chem Eng 18 (1994) 563–578.

[4] P.M. Castro, I.E. Grossmann, Generalized disjunctive programming as a systematic modeling framework to derive scheduling formulations, Ind Eng Chem Res 51 (2012) 5781–5792.

[5] I.E. Grossmann, F. Trespalacios, Systematic modeling of discrete-continuous optimization models through generalized disjunctive programming, AIChE J 59 (2013) 3276–3295.

[6] H. Mostafaei, P.M. Castro, A. Ghaffari-Hadigheh, A novel monolithic MILP framework for lot-sizing and scheduling of multiproduct treelike pipeline networks, Ind Eng Chem Res 54 (2015) 9202–9221.


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