Line-haul feeder location-routeing problem: mathematical model and heuristic algorithm

Ali Nadizadeh, Ali Sabzevari Zadeh, Mahdi Bashiri

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


This study proposes a mathematical formulation and solution approach for a novel extension of the location-routeing problem (LRP), namely line-haul feeder LRP (LFLRP), where large vehicles (trucks) are synchronised with small vehicles (motorcycles) throughout delivery process. Customers are visited by site-dependent vehicles such that those not accessible by trucks must be served by motorcycles. The LFLRP is formulated as a mixed-integer linear programming model, and two efficient heuristic algorithms called EHA and Enhanced-EHA are developed to solve the problem. Experimental results show that the proposed algorithms can provide near-optimal solutions for 18 randomly generated small-scale LFLRP test instances and best-known solutions for 12 out of 19 large-scale standard LRP test instances in reasonable computation time. A cost-benefit analysis also indicates that the LFLRP model can considerably reduce total costs compared to equivalent standard LRP formulations. To provide managerial insights, a case study and sensitivity analysis of key parameters are conducted.
Original languageEnglish
Article number2087787
Number of pages38
JournalTransportmetrica A: Transport Science
Issue number3
Early online date20 Jun 2022
Publication statusPublished - 27 May 2023

Bibliographical note

Publisher Copyright:
© 2022 Hong Kong Society for Transportation Studies Limited.


  • Location-routeing problem
  • feeder routeing
  • mixed-integer linear programming
  • efficient heuristic algorithm


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