Soft Computing

, Volume 23, Issue 4, pp 1375–1391 | Cite as

A bi-objective fleet size and mix green inventory routing problem, model and solution method

  • Mehdi AlinaghianEmail author
  • Mohsen Zamani
Methodologies and Application


Inventory routing problem (IRP) is one of the most important logistics problems; in this type of problems, decision maker usually has the option to use several types of vehicles to form a fleet with appropriate size and composition in order to minimize both inventory and transportation costs. Meanwhile, the increasing fuel consumption and its economic and environmental impacts mean that this issue must also be incorporated into the routing problems. This paper proposes a new bi-objective model for green inventory routing problem with the heterogeneous fleet. The objectives of the proposed model are (I) to reduce the emissions and (II) to minimize the fleet size, vehicle type, routing, and inventory costs. Given the NP-hard nature of the assessed problem, a bi-objective meta-heuristic algorithm based on the quantum evolutionary algorithm is proposed to achieve these objectives. To evaluate the performance of the proposed algorithm, its results are compared with the results of the exact method and Non-dominated Sorting Genetic Algorithm II (NSGAII). The results of these comparisons indicate the better performance of the proposed algorithm.


Multi-objective optimization Pollutant emissions Fuel consumption The fleet size and mix IRP Quantum evolutionary algorithm NSGAII 



This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringIsfahan University of TechnologyIsfahanIran

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