# Scenario-Based Location Arc Routing Problems: Introducing Mathematical Models

• Alireza Amini
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)

## Abstract

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.

## Keywords

Location arc routing Mathematical model Scenario-based Regret

## References

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):629–643
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):189–208
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):291–302
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):649–672
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):125–141
9. 9.
Prodhon C, Prins C (2014) A survey of recent research on location-routing problems. Eur J Oper Res 238(1):1–17
10. 10.
Riquelme-Rodríguez JP, Gamache M, Langevin A (2016) Location arc routing problem with inventory constraints. Comput Oper Res 76:84–94
11. 11.
Rui BL, Fea Plastria (2014) Location-arc routing problem: heuristic approaches and test instances. Comput Oper Res 43(3):309–317

© Springer International Publishing AG 2018

## Authors and Affiliations

• Alireza Amini
• 1