Scenario-Based Location Arc Routing Problems: Introducing Mathematical Models

  • Alireza Amini
  • Reza Tavakkoli-MoghaddamEmail author
  • Sadoullah Ebrahimnejad
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)


A location arc routing problem (LARP) is an important issue that finds the best locations of depots and routing simultaneously. It deals with a routing problem, in which demands are on arcs instead of nodes. Additionally, parameters may not be deterministic in real problems. Thus, this paper addresses an uncertain LARP through developing a deterministic mathematical model regarding to the respective literature and employing two scenario-based approaches. The objectives of the model are to minimize the maximum regret and minimize the mean and deviation of the objective function value (OFV). A numerical example is generated and the results analyze the performance of scenario-based models.


Location arc routing Mathematical model Scenario-based Regret 


  1. 1.
    Beullens P, Muyldermans L, Cattrysse D et al (2003) A guided local search heuristic for the capacitated arc routing problem. Eur J Oper Res 147(3):629–643MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bodin L, Levy L (1989) The arc oriented location routing problem. INFOR Inf Syst Oper Res 27(1):74–94Google Scholar
  3. 3.
    Doulabi SHH, Seifi A (2013) Lower and upper bounds for location-arc routing problems with vehicle capacity constraints. Eur J Oper Res 224(1):189–208MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Drexl M, Schneider M (2014) A Survey of the Standard Location-Routing Problem. Publications of Darmstadt Technical University Institute for Business StudiesGoogle Scholar
  5. 5.
    Ghiani G, Laporte G (1999) Eulerian location problems. Networks 34(4):291–302MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ghiani G, Laporte G (2001) Location-arc routing problems. Opserach 38(2):151–159Google Scholar
  7. 7.
    Nagy G, Salhi S (2007) Location-routing: issues, models and methods. Eur J Oper Res 177(2):649–672MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Pia AD, Filippi C (2006) A variable neighborhood descent algorithm for a real waste collection problem with mobile depots. Int Trans Oper Res 13(2):125–141CrossRefzbMATHGoogle Scholar
  9. 9.
    Prodhon C, Prins C (2014) A survey of recent research on location-routing problems. Eur J Oper Res 238(1):1–17MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Riquelme-Rodríguez JP, Gamache M, Langevin A (2016) Location arc routing problem with inventory constraints. Comput Oper Res 76:84–94MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Rui BL, Fea Plastria (2014) Location-arc routing problem: heuristic approaches and test instances. Comput Oper Res 43(3):309–317MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Alireza Amini
    • 1
  • Reza Tavakkoli-Moghaddam
    • 2
    Email author
  • Sadoullah Ebrahimnejad
    • 3
  1. 1.School of Industrial Engineering, South Tehran BranchIslamic Azad UniversityTehranIran
  2. 2.School of Industrial Engineering, College of EngineeringUniversity of TehranTehranIran
  3. 3.Department of Industrial Engineering, Karaj BranchIslamic Azad UniversityKarajIran

Personalised recommendations