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A survey of the standard location-routing problem

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Abstract

In this paper, we define the standard LRP as a deterministic, static, discrete, single-echelon, single-objective location-routing problem in which each customer (vertex) must be visited exactly once for the delivery of a good from a facility, and in which no inventory decisions are relevant. We review the literature on the standard LRP published since the survey by Nagy and Salhi appeared in 2006. We provide concise paper excerpts that convey the central ideas of each work, discuss recent developments in the field, provide a numerical comparison of the most successful heuristic algorithms, and list promising topics for further research.

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Acknowledgements

The second author was partially funded by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. DR 963/2-1.

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Authors and Affiliations

  1. Deutsche Post Chair of Optimization of Distribution Networks, RWTH Aachen University, Aachen, Germany

    Michael Schneider

  2. Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University, Mainz, Germany

    Michael Drexl

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Correspondence to Michael Schneider.

Appendices

Appendix 1: Summary of abbreviations

BKS:

Best known solution

CFLP:

Capacitated FLP

ELS:

Evolutionary LS

ENS:

Expanding neighborhood search

ESPPRC:

Elementary shortest path problem with resource constraints

FLP:

Facility location problem

GA:

Genetic algorithm

GRASP:

Greedy randomized adaptive search procedure

GTS:

Granular TS

ILS:

Iterated LS

IP:

Integer program(ming)

LARP:

Location arc-routing problem

LP:

Linear program(ming)

LR:

Lagrangian relaxation

LRP:

Location-routing problem

LS:

Local search

M(C)DVRP:

Multi-depot VRP (with capacitated depots)

MIP:

Mixed IP

PR:

Path relinking

RECWA:

Randomized extended Clarke and Wright algorithm

SA:

Simulated annealing

SSCFLP:

Single-source CFLP

TS:

Tabu search

TSP:

Traveling salesman problem

VND:

Variable neighborhood descent

VNS:

Variable neighborhood search

VRP:

Vehicle routing problem

Appendix 2: BKS for popular benchmark sets

Table 3 Best known solutions as of spring 2017 for the benchmark sets TB, PPW, and B
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Schneider, M., Drexl, M. A survey of the standard location-routing problem. Ann Oper Res 259, 389–414 (2017). https://doi.org/10.1007/s10479-017-2509-0

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