Skip to main content

Advertisement

Log in

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

  • Methodologies and Application
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Adulyasak Y, Cordeau J-F, Jans R (2013) Formulations and branch-and-cut algorithms for multivehicle production and inventory routing problems. INFORMS J Comput 26:103–120

    Article  MathSciNet  MATH  Google Scholar 

  • Ahmadi Javid A, Azad N (2010) Incorporating location, routing and inventory decisions in supply chain network design. Transp Res Part E Logist Transp Rev 46:582–597

    Article  Google Scholar 

  • Alinaghian M, Ghazanfari M, Salamatbakhsh A, Norouzi N (2012) A new competitive approach on multi-objective periodic vehicle routing problem. Int J Appl Oper Res 1:33–41

    MATH  Google Scholar 

  • Aydın N (2014) A genetic algorithm on inventory routing problem. EMAJ Emerg Mark J 3:59–66

    Article  Google Scholar 

  • Bell WJ, Dalberto LM, Fisher ML, Greenfield AJ, Jaikumar R, Kedia P et al (1983) Improving the distribution of industrial gases with an on-line computerized routing and scheduling optimizer. Interfaces 13:4–23

    Article  Google Scholar 

  • Bertazzi L, Bosco A, Guerriero F, Laganà D (2013) A stochastic inventory routing problem with stock-out. Transp Res Part C Emerg Technol 27:89–107

    Article  Google Scholar 

  • Campbell AM, Savelsbergh MW (2004) A decomposition approach for the inventory-routing problem. Transp Sci 38:488–502

    Article  Google Scholar 

  • Chrysochoou EC, Ziliaskopoulos AK, Lois A (2015) An exact algorithm for the stochastic inventory routing problem with transhipment. In: Transportation research board 94th annual meeting

  • Cohon JL (2013) Multiobjective programming and planning. Courier Corporation, North Chelmsford

    MATH  Google Scholar 

  • Deb K (2014) Multi-objective optimization. In: Burke E, Kendall G (eds) Search methodologies. Springer, Boston, MA

    Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197

    Article  Google Scholar 

  • Demir E, Bektaş T, Laporte G (2014) The bi-objective pollution-routing problem. Eur J Oper Res 232:464–478

    Article  MathSciNet  MATH  Google Scholar 

  • Deng W, Zhao H, Liu J, Yan X, Li Y, Yin L et al (2015) An improved CACO algorithm based on adaptive method and multi-variant strategies. Soft Comput 19:701–713

    Article  Google Scholar 

  • Deng W, Zhao H, Zou L, Li G, Yang X, Wu D (2017a) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21:4387–4398

  • Deng W, Zhao H, Yang X, Xiong J, Sun M, Li B (2017b) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302

  • Golden B, Assad A, Levy L, Gheysens F (1984) The fleet size and mix vehicle routing problem. Comput Oper Res 11:49–66

    Article  MATH  Google Scholar 

  • Gu B, Sun X, Sheng VS (2017) Structural minimax probability machine. IEEE Trans Neural Netw Learn Syst 28:1646–1656

    Article  MathSciNet  Google Scholar 

  • Halim H, Moin N (2014) Solving inventory routing problem with backordering using Artificial Bee Colony. In: International conference on industrial engineering and engineering management (IEEM), 2014 IEEE, pp 913–917

  • Han K-H, Kim J-H (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6:580–593

    Article  MathSciNet  Google Scholar 

  • Han K-H, Kim J-H (2004) Quantum-inspired evolutionary algorithms with a new termination criterion, Hε gate, and two-phase scheme. IEEE Trans Evol Comput 8:156–169

    Article  Google Scholar 

  • Huang S-H, Lin P-C (2010) A modified ant colony optimization algorithm for multi-item inventory routing problems with demand uncertainty. Transp Res Part E Logist Transp Rev 46:598–611

    Article  Google Scholar 

  • Jolai F, Amalnick MS, Alinaghian M, Shakhsi-Niaei M, Omrani H (2011) A hybrid memetic algorithm for maximizing the weighted number of just-in-time jobs on unrelated parallel machines. J Intell Manuf 22:247–261

    Article  Google Scholar 

  • Kaye P, Laflamme R, Mosca M (2007) An introduction to quantum computing. Oxford University Press, Oxford

    MATH  Google Scholar 

  • Koç Ç, Bektaş T, Jabali O, Laporte G (2014) The fleet size and mix pollution-routing problem. Transp Res Part B Methodol 70:239–254

    Article  MATH  Google Scholar 

  • Kong Y, Zhang M, Ye D (2017) A belief propagation-based method for task allocation in open and dynamic cloud environments. Knowl Based Syst 115:123–132

    Article  Google Scholar 

  • Kopfer H (2013) Emissions minimization vehicle routing problem in dependence of different vehicle classes. In: Kreowski H-J, Scholz-Reiter B, Thoben K-D (eds) Dynamics in Logistics. Springer, Berlin, Heidelberg, pp 49–58

    Chapter  Google Scholar 

  • Kwon YJ, Choi YJ, Lee DH (2013) Heterogeneous fixed fleet vehicle routing considering carbon emission. Transp Res Part D Transp Environ 23:81–89

    Article  Google Scholar 

  • Lee HL, Seungjin W (2008) The whose, where and how of inventory control design. Supply Chain Manag Rev 12:22–29

    Google Scholar 

  • Liu Q, Cai W, Shen J, Fu Z, Liu X, Linge N (2016) A speculative approach to spatial-temporal efficiency with multi-objective optimization in a heterogeneous cloud environment. Secur Commun Netw 9:4002–4012

    Article  Google Scholar 

  • Mavrotas G (2009) Effective implementation of the \(\varepsilon \)-constraint method in multi-objective mathematical programming problems. Appl Math Comput 213:455–465

    MathSciNet  MATH  Google Scholar 

  • Mirzapour Al-e-hashem SMJ, Rekik Y (2014) Multi-product multi-period Inventory Routing Problem with a transshipment option: a green approach. Int J Prod Econ 157:80–88

    Article  Google Scholar 

  • Moin N, Salhi S, Aziz N (2011) An efficient hybrid genetic algorithm for the multi-product multi-period inventory routing problem. Int J Prod Econ 133:334–343

    Article  Google Scholar 

  • Montgomery DC (2017) Design and analysis of experiments. Wiley

  • Niakan F, Rahimi M (2015) A multi-objective healthcare inventory routing problem; a fuzzy possibilistic approach. Transp Res Part E Logist Transp Rev 80:74–94

    Article  Google Scholar 

  • Platel MD, Schliebs S, Kasabov N (2007) A versatile quantum-inspired evolutionary algorithm. In: IEEE congress on evolutionary computation, 2007. CEC 2007, pp 423–430

  • Raa B, Aghezzaf E-H (2008) Designing distribution patterns for long-term inventory routing with constant demand rates. Int J Prod Econ 112:255–263

    Article  Google Scholar 

  • Rakke JG, Andersson H, Christiansen M, Desaulniers G (2014) A new formulation based on customer delivery patterns for a maritime inventory routing problem. Transp Sci 49:384–401

    Article  Google Scholar 

  • Rong H, Ma T, Tang M, Cao J (2017) A novel subgraph \(K^{+}\)-isomorphism method in social network based on graph similarity detection. Soft Comput. doi:10.1007/s00500-017-2513-y

  • Savelsbergh M, Song J-H (2007) Inventory routing with continuous moves. Comput Oper Res 34:1744–1763

    Article  MathSciNet  MATH  Google Scholar 

  • Sbihi A, Eglese RW (2007) Combinatorial optimization and green logistics. 4OR Q J Oper Res 5:99–116

  • Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization, TIC Document1995

  • Shao S, Huang GQ (2014) A SHIP inventory routing problem with heterogeneous vehicles under order-up-to level policies. In: Proceedings of IIE annual conference, p 1106

  • Shen Z-JM, Coullard C, Daskin MS (2003) A joint location-inventory model. Transp Sci 37:40–55

    Article  Google Scholar 

  • Soysal M, Bloemhof-Ruwaard JM, Haijema R, van der Vorst JG (2015) Modeling an Inventory Routing Problem for perishable products with environmental considerations and demand uncertainty. Int J Prod Econ 164:118–133

    Article  Google Scholar 

  • Trudeau P, Dror M (1992) Stochastic inventory routing: route design with stockouts and route failures. Transp Sci 26:171–184

    Article  MATH  Google Scholar 

  • Xue Y, Jiang J, Zhao B, Ma T (2017) A self-adaptive artificial bee colony algorithm based on global best for global optimization. Soft Comput. doi:10.1007/s00500-017-2547-1

  • Yang P-C, Wee H-M (2002) A single-vendor and multiple-buyers production-inventory policy for a deteriorating item. Eur J Oper Res 143:570–581

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang G (2011) Quantum-inspired evolutionary algorithms: a survey and empirical study. J Heuristics 17:303–351

    Article  MATH  Google Scholar 

  • Zhang J, Wang W, Zhao Y, Cattani C (2012) Multiobjective quantum evolutionary algorithm for the vehicle routing problem with customer satisfaction. Math Probl Eng 2012:1–19

    MathSciNet  MATH  Google Scholar 

  • Zhou A, Qu B-Y, Li H, Zhao S-Z, Suganthan PN, Zhang Q (2011) Multiobjective evolutionary algorithms: a survey of the state of the art. Swarm Evol Comput 1:32–49

    Article  Google Scholar 

  • Zitzler E, Thiele L (1998) Multi-objective optimization using evolutionary algorithms—a comparative case study. In: International conference on parallel problem solving from nature. Springer, Berlin, Heidelberg, pp 292–301

Download references

Acknowledgements

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mehdi Alinaghian.

Ethics declarations

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.

Additional information

Communicated by V. Loia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alinaghian, M., Zamani, M. A bi-objective fleet size and mix green inventory routing problem, model and solution method. Soft Comput 23, 1375–1391 (2019). https://doi.org/10.1007/s00500-017-2866-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-017-2866-2

Keywords

Navigation