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Maximum Concurrent Flow with Incomplete Data

  • Pierre-Olivier BauguionEmail author
  • Claudia D’Ambrosio
  • Leo Liberti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10856)

Abstract

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.

Keywords

Maximum concurrent flow Multi-commodity flow problems Incomplete data Unknown data Uncertainty Inverse optimization Transportation systems 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Pierre-Olivier Bauguion
    • 1
    Email author
  • Claudia D’Ambrosio
    • 2
  • Leo Liberti
    • 2
  1. 1.IRT SystemXPalaiseauFrance
  2. 2.CNRS LIX, Ecole PolytechniquePalaiseauFrance

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