Skip to main content
Log in

A mathematical model and a solving procedure for multi-depot vehicle routing problem with fuzzy time window and heterogeneous vehicle

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

One of the most important and yet complex decision-making problems in the area of transportation programming issues is vehicle routing problem. There are various exact, heuristic, and metaheuristic methods presented for solving different vehicle routing problems. In this manuscript, a mathematical model and a new heuristic solution method are proposed for solving multi-depot vehicle routing problem with time windows and different types of vehicles. In this problem, depots must serve customers between their fuzzy time windows with vehicles having different capacities, velocities, and costs. For this purpose, the mathematical model for multi-depot routing problem is developed to consider the mentioned circumstances. The objectives of this model is travel distance reduction and customers’ service level increscent which leads to cost and service time reduction. For complexity of this problem and much computational time of exact solutions of developed model, a heuristic approach is proposed. This systematic approach has some steps as: customer clustering, routing, vehicle type determination, scheduling, and routes improvement using simulated annealing and customer service level improvement. The efficiency of the proposed method is analyzed by a case study in ISACO Co. Results show that the method is efficient and applicable in industries.

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.

Similar content being viewed by others

References

  1. Balakrishnan N (1993) Simple heuristic for vehicle routing problem with soft time windows. Oper Res Soc 44:279–287

    Article  MATH  Google Scholar 

  2. Balseiro SR, Loiseau I, Ramonet J (2011) An Ant Colony algorithm hybridized with insertion heuristics for the Time Dependent Vehicle Routing Problem with Time Windows. Comput Oper Res 38:954–966

    Article  MathSciNet  MATH  Google Scholar 

  3. Calvete HI, Gale C, Oliveros M, Sanchez-Valverde B (2007) A goal programming approach to vehicle routing problem with soft time windows. Eur J Oper Res 44:1720–1733

    Article  MathSciNet  Google Scholar 

  4. Chiang WC, Russell RA (2004) A metaheuristic for vehicle routing problem with soft time windows. Oper Res Soc 55:1298–1310

    Article  MATH  Google Scholar 

  5. Chiang WC, Russell RA (2004) Integrating purchasing and routing in a propane gas supply chain. Eur J Oper Res 154:710–729

    Article  MATH  Google Scholar 

  6. Dondo R, Cerda J (2007) A cluster-based optimization approach for the multi-depot heterogeneous fleet vehicle routing problem with time windows. Eur J Oper Res 176:1478–1507

    Article  MATH  Google Scholar 

  7. Farhang Moghadam B, Ruiz R, Sadjadi SR (2012) Vehicle routing problem with uncertain demands: an advanced particle swarm algorithm. Comput Ind Eng 62:306–317

    Article  Google Scholar 

  8. Ferland JA, Fortin L (1989) vehicle routing with sliding time windows. Eur J Oper Res 38:213–226

    Article  MATH  Google Scholar 

  9. Gillet BE, Miller LR (1974) A heuristic algorithm for vehicle dispatching problem. J Oper Res 22:340–349

    Article  Google Scholar 

  10. Giosa ID, Tansini IL, Viera IC (2002) New assignment algorithm for multi-depot vehicle routing problem. J Oper Res Soc 53:977–984

    Article  MATH  Google Scholar 

  11. Goksal FP, Karaoglan I, Altiparmak F (2013) A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery. Comput Ind Eng 66:39–53

  12. Ho W, George TS, Ping J, Henry CW (2008) A hybrid genetic algorithm for the multi-depot vehicle routing problem. Eng Appl Artif Intell 21:548–557

    Article  Google Scholar 

  13. Hong L (2012) An improved LNS algorithm for real time vehicle routing problem with time windows. Comput Oper Res 39:151–163

    Article  MATH  Google Scholar 

  14. Mirabi M, Fatemi Ghomi SMT, Jolai F (2010) Efficient stochastic hybrid heuristics for the multi-depot vehicle routing problem. Robot Comput Integr Manuf 26:564–569

    Article  Google Scholar 

  15. Salhi S, Sari M (1997) A multi-level composite search heuristic for the multi depot vehicle fleet mix problem. Eur J Oper Res 103:95–112

    Article  MATH  Google Scholar 

  16. Savelsbergh M (1985) Local search for routing problems with time windows. Ann Oper Res 4:285–305

    Article  MathSciNet  Google Scholar 

  17. Sexton T, Choi Y (1986) Pick-up and delivery of partial loads with soft time windows. Am J Math Manag Sci 6:396–398

    Google Scholar 

  18. Solomon MM (1987) Algorithms for the vehicle routing scheduling problem with time window constraints. Oper Res 35:245–265

    Article  Google Scholar 

  19. Solomon MM, Desrosiers J (1988) Time windows constrained routing and scheduling problems. Transp Sci 22:1–13

    Article  MathSciNet  MATH  Google Scholar 

  20. Sur B, Heany H, Gyu C, Meny G (2007) Integrated GA-VRP solver for multi depot system. Comput Ind Eng 53:233–240

    Article  Google Scholar 

  21. Tan KC, Cheong CY, Goh CK (2007) Solving multi objective vehicle routing problem with stochastic demand via-evolutionary computation. Eur J Oper Res 177:813–839

    Article  MATH  Google Scholar 

  22. Tang J, Pan Z, Richard YK, Lau H (2009) Vehicle routing problem with fuzzy time windows. Fuzzy Set Syst 160:683–695

    Article  MATH  Google Scholar 

  23. Tillman FA, Cain TM (1972) An upper bound algorithm for the single and multiple-terminal delivery problem. Manag Sci 18:662–682

    Article  Google Scholar 

  24. Wang HF, Chen YY (2012) A genetic algorithm for the simultaneous delivery and pickup problems with time window. Comput Ind Eng 62:84–95

    Article  Google Scholar 

  25. Wang HF, Wen YP (2002) Time-constrained Chinese postman problems. Comput Mathe Appl 44:375–387

    Article  MathSciNet  MATH  Google Scholar 

  26. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

  27. Zheng Y, Liu B (2006) Fuzzy vehicle routing model with credibility measure and its hybrid intelligent algorithm. Appl Math Comput 176:673–683

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vahid Mahdavi Asl.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Adelzadeh, M., Mahdavi Asl, V. & Koosha, M. A mathematical model and a solving procedure for multi-depot vehicle routing problem with fuzzy time window and heterogeneous vehicle. Int J Adv Manuf Technol 75, 793–802 (2014). https://doi.org/10.1007/s00170-014-6141-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-014-6141-8

Keywords

Navigation