A Stochastic Single Vehicle Routing Problem with a Predefined Sequence of Customers and Collection of Two Similar Materials

Abstract

We suppose that a vehicle visits N ordered customers in order to collect from them two similar but not identical materials. The actual quantity and the actual type of material that each customer possesses become known only when the vehicle arrives at the customer’s location. It is assumed that the vehicle has two compartments. We name these compartments, Compartment 1 and Compartment 2. It is assumed that Compartment 1 is suitable for loading Material 1 and Compartment 2 is suitable for loading Material 2. However it is permitted to load items of Material 1 into Compartment 2 and items of Material 2 into Compartment 1. These actions cause extra costs that are due to extra labor. It is permissible for the vehicle to interrupt its route and go to the depot to unload the items of both materials. The costs for travelling from each customer to the next one and the costs for travelling from each customer to the depot are known. The objective is to find the routing strategy that minimizes the total expected cost among all possible strategies for servicing all customers. A dynamic programming algorithm is designed for the determination of the routing strategy that minimizes the total expected cost among all possible strategies. The structure of optimal routing strategy is characterized by a set of critical numbers for each customer.

This is a preview of subscription content, access via your institution.

References

  1. Clarke G, Wright JR (1964) Scheduling of vehicle routing problem from a central depot to a number of delivery points. Oper Res 12:568–581

    Article  Google Scholar 

  2. Dantzig G, Ramser R (1959) The truck dispatching problem. Manage Sci 6:80–91

    MathSciNet  Article  Google Scholar 

  3. Dimitrakos TD, Kyriakidis EG (2015) A single vehicle routing problem with pickups and deliveries, continuous random demands and predefined customer order. Eur J Oper Res 244:990–993

    MathSciNet  Article  Google Scholar 

  4. Elgesem AS, Skogen ES, Wang X, Fagerholt K (2018) A traveling salesman problem with pickups and deliveries and stochastic travel times: An application from chemical shipping. Eur J Oper Res 269:844–859

    MathSciNet  Article  Google Scholar 

  5. Gendreau M, Laporte G, Seguin R (1996) Stochastic vehicle routing. Eur J Oper Res 88:3–12

    Article  Google Scholar 

  6. Haugland D, Ho SC, Laporte G (2007) Designing delivery districts for the vehicle routing problem with stochastic demands. Eur J Oper Res 180:997–1010

    MathSciNet  Article  Google Scholar 

  7. Kyriakidis EG, Dimitrakos TD (2008) Single vehicle routing problem with a predefined customer sequence and stochastic continuous demands. Math Sci 33:148–152

    MathSciNet  MATH  Google Scholar 

  8. Kyriakidis EG, Dimitrakos TD (2013) A vehicle routing problem with a predefined customer sequence, stochastic demands and penalties for unsatisfied demands. Proceedings of 5th International Conference on Applied Operational Research Lect Notes Manage Sci 5:10–17

    Google Scholar 

  9. Kyriakidis EG, Dimitrakos TD, Karamatsoukis CC (2019) Optimal delivery of two similar products to N ordered customers with product preferences. Int J Prod Econ 209:194–204

    Article  Google Scholar 

  10. Markov I, Bierlaire M, Cordeau JF, Maknoon Y, Varone S (2020) Waste collection inventory routing with non-stationary stochastic demands. Comput Oper Res 113:Article number 104798

  11. Minis I, Tatarakis A (2011) Stochastic single vehicle routing problem with delivery and pickup and a predefined customer sequence. Eur J Oper Res 213:37–51

    Article  Google Scholar 

  12. Nguyen VA, Jiang J, Ng KM, Teo KM (2016) Satisfying measure approach for vehicle routing problem with time windows under uncertainty. Eur J Oper Res 248:404–414

    Article  Google Scholar 

  13. Pandelis DG, Kyriakidis EG, Dimitrakos TD (2012) Single vehicle routing problems with a predefined customer sequence, compartmentalized load and stochastic demands. Eur J Oper Res 217:324–332

    MathSciNet  Article  Google Scholar 

  14. Pandelis DG, Karamatsoukis CC, Kyriakidis EG (2013a) Single vehicle routing problems with a predefined customer order, unified load and stochastic discrete demands. Probab Eng Inf Sci 27(1):1–23

    MathSciNet  Article  Google Scholar 

  15. Pandelis DG, Karamatsoukis CC, Kyriakidis EG (2013b) Finite and infinite-horizon single vehicle routing problems with a predefined customer sequence and pickup and delivery. Eur J Oper Res 231:577–586

    MathSciNet  Article  Google Scholar 

  16. Pillac V, Gendreau M, Gueret C, Megaglia A (2013) A review of dynamic vehicle routing problems. Eur J Oper Res 225:1–11

    MathSciNet  Article  Google Scholar 

  17. Psaraftis HN, Wen M, Kontovas CA (2016) Dynamic vehicle routing problems: Three decades and counting. Networks 67:3–31

    MathSciNet  Article  Google Scholar 

  18. Ritzinger U, Puchinger J, Richard HF (2016) A survey on dynamic and stochastic vehicle routing problems. Int J Prod Res 54(1):215–231

    Article  Google Scholar 

  19. Sipser M (2013) Introduction to the theory of computation, 3rd edn. Cengage Learning, Boston

    Google Scholar 

  20. Tatarakis A, Minis I (2009) Stochastic single vehicle routing with a predefined customer sequence and multiple depot returns. Eur J Oper Res 197:557–571

    MathSciNet  Article  Google Scholar 

  21. Toth P, Vigo D (eds) (2014) The vehicle routing problem. Problems, methods and applications, 2nd edn. MOS-SIAM, Philadelphia

    Google Scholar 

  22. Tsirimpas P, Tatarakis A, Minis I, Kyriakidis EG (2008) Single vehicle routing with a predefined customer sequence and multiple depot returns. Eur J Oper Res 187:483–495

    MathSciNet  Article  Google Scholar 

  23. Yang W-H, Mathur K, Ballou RH (2000) Stochastic vehicle routing problem with restocking. Transport Sci 34:99–112

    Article  Google Scholar 

  24. Zhang J, Lam WHK, Chen BY (2016) On-time delivery probabilistic models for the vehicle routing problem with stochastic demands and time windows. Eur J Oper Res 249:144–154

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank a reviewer for useful suggestions that improved the presentation of the paper. The author Epaminondas G. Kyriakidis has been financed by the research program EP-3042-01 (RC/AUEB).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Epaminondas G. Kyriakidis.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kyriakidis, E.G., Dimitrakos, T.D. & Karamatsoukis, C.C. A Stochastic Single Vehicle Routing Problem with a Predefined Sequence of Customers and Collection of Two Similar Materials. Methodol Comput Appl Probab 22, 1559–1582 (2020). https://doi.org/10.1007/s11009-019-09759-9

Download citation

Keywords

  • Stochastic dynamic programming
  • Vehicle routing problem

Mathematics Subject Classification (2010)

  • Primary 90C39
  • Secondary 90B06