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Maximum concurrent flow with incomplete data. (English) Zbl 1403.90629

Lee, Jon (ed.) et al., Combinatorial optimization. 5th international symposium, ISCO 2018, Marrakesh, Morocco, April 11–13, 2018. Revised selected papers. Cham: Springer (ISBN 978-3-319-96150-7/pbk; 978-3-319-96151-4/ebook). Lecture Notes in Computer Science 10856, 77-88 (2018).
Summary: The maximum concurrent flow problem (MCFP) is often used in the planning of transportation and communication networks. We discuss here the MCFP with incomplete data. We call this new problem the incomplete maximum concurrent flow problem (IMCFP). The main objective of IMCFP is to complete the missing information assuming the known and unknown data form a MCFP and one of its optimal solutions. We propose a new solution technique to solve the IMCFP which is based on a linear programming formulation involving both primal and dual variables, which optimally decides values for the missing data so that they are compatible with a set of scenarios of different incomplete data sets. We prove the correctness of our formulation and benchmark it on many different instances.
For the entire collection see [Zbl 1392.90003].

MSC:

90C35 Programming involving graphs or networks
90C27 Combinatorial optimization
90B06 Transportation, logistics and supply chain management
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