Advertisement

Sādhanā

, 44:39 | Cite as

A mixed integer linear programming model for the vehicle routing problem with simultaneous delivery and pickup by heterogeneous vehicles, and constrained by time windows

  • Sakthivel Madankumar
  • Chandrasekharan RajendranEmail author
Article
  • 10 Downloads

Abstract

In this work, we consider the Vehicle Routing Problem with Simultaneous Delivery and Pickup, and constrained by time windows, to improve the performance and responsiveness of the supply chain by transporting goods from one location to another location in an efficient manner. In this class of problem, each customer demands a quantity to be delivered as a part of the forward supply service and another quantity to be picked up as a part of the reverse recycling service, and the complete service has to be done simultaneously in a single visit of a vehicle, and the objective is to minimize the total cost, which includes the traveling cost and dispatching cost for operating vehicles. We propose a Mixed Integer Linear Programming (MILP) model for solving this class of problem. In order to evaluate the performance of the proposed MILP model, a comparison study is made between the proposed MILP model and an existing MILP model available in the literature, with the consideration of heterogeneous vehicles. Our study indicates that the proposed MILP model gives tighter lower bound and also performs better in terms of the execution time to solve each of the randomly generated problem instances, in comparison with the existing MILP model. In addition, we also compare the proposed MILP model (assuming homogeneous vehicles) with the existing MILP model that also considers homogeneous vehicles. The results of the computational evaluation indicate that the proposed MILP model gives much tighter lower bound, and it is competitive to the existing MILP model in terms of the execution time to solve each of the randomly generated problem instances.

Keywords

Supply chain transportation vehicle routing problem simultaneous delivery and pickup time windows integer programming model 

Notes

Acknowledgement

We are thankful to the reviewers and the Editor for their valuable comments and suggestions to improve our manuscript.

References

  1. 1.
    Chopra S and Meindl P 2007 Supply chain management: strategy, planning and operation. New Jersey: Pearson Prentice HallGoogle Scholar
  2. 2.
    Toth P and Vigo D 2002 The vehicle routing problem. In: SIAM Monographs on Discrete Mathematics and Applications. Philadelphia, PA, USA: SIAMGoogle Scholar
  3. 3.
    Parragh S N, Doerner K F and Hartl R F 2008 A survey on pickup and delivery problems. J. Betriebswirtschaft 58: 21–51CrossRefGoogle Scholar
  4. 4.
    Wang H F and Chen Y Y 2012 A genetic algorithm for the simultaneous delivery and pickup problems with time window. Comput. Ind. Eng. 62: 84–95CrossRefGoogle Scholar
  5. 5.
    Min H 1989 The multiple vehicle routing problem with simultaneous delivery and pick-up points. Transp. Res. A Gen. 23: 377–386CrossRefGoogle Scholar
  6. 6.
    Dethloff J 2002 Relation between vehicle routing problems: an insertion heuristic for the vehicle routing problem with simultaneous delivery and pick-up applied to the vehicle routing problem with backhauls. J. Oper. Res. Soc. 53: 115–118CrossRefGoogle Scholar
  7. 7.
    Ganesh K and Narendran T T 2008 TASTE: a two-phase heuristic to solve a routing problem with simultaneous delivery and pick-up. Int. J. Adv. Manuf. Technol. 37: 1221–1231CrossRefGoogle Scholar
  8. 8.
    Ai T J and Kachitvichyanukul V 2009 A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery. Comput. Oper. Res. 36: 1693–1702CrossRefGoogle Scholar
  9. 9.
    Liu R, Xie X, Augusto V and Rodriguez C 2013 Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care. Eur. J. Oper. Res. 230: 475–486MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wang C, Mu D, Zhao F and Sutherland J W 2015 A parallel simulated annealing method for the vehicle routing problem with simultaneous pickup–delivery and time windows. Comput. Ind. Eng. 83: 111–122CrossRefGoogle Scholar
  11. 11.
    Kallehauge B, Larsen J, Madsen O B and Solomon M M 2005. Vehicle routing problem with time windows. In: Desaulniers G, Desrosiers J and Solomon M M (Eds.) Column Generation. New York: Springer, pp. 67–98CrossRefGoogle Scholar
  12. 12.
    Polat O, Kalayci C B, Kulak O and Günther H O 2015 A perturbation based variable neighborhood search heuristic for solving the Vehicle Routing Problem with Simultaneous Pickup and Delivery with Time Limit. Eur. J. Oper. Res. 242: 369–382MathSciNetCrossRefGoogle Scholar
  13. 13.
    Solomon M M 1987 Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper. Res. 35: 254–265MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ramanathan R, George J and Ramanathan U 2014 The role of logistics in e-commerce transactions: an exploratory study of customer feedback and risk. In: Ramanathan U and Ramanathan R (Eds.) Supply Chain Strategies, Issues and Models. London: Springer, pp. 221–233CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  • Sakthivel Madankumar
    • 1
  • Chandrasekharan Rajendran
    • 1
    Email author
  1. 1.Department of Management StudiesIndian Institute of Technology MadrasChennaiIndia

Personalised recommendations