Advertisement

A two-level evolutionary algorithm for solving the petrol station replenishment problem with periodicity constraints and service choice

  • Nasr Al-Hinai
  • Chefi TrikiEmail author
S.I.: CLAIO 2016
  • 45 Downloads

Abstract

This paper addresses the petrol station replenishment problem with periodicity constraints and introduces the frequency service choice as a decision variable. We present a mathematical optimization model for the problem and we develop first a simple heuristic method that is able to handle the complexity of the problem and then two metaheuristic approaches based on a novel two-level evolutionary algorithm. The first level deals with the periodicity and frequency selection of the visits to the petrol stations. The second level of evolution assigns the stations to the tank-trucks such that the total traveled distance is minimized. The effectiveness of the proposed approaches has been tested by means of a comprehensive experimental study by using first a set of randomly generated test cases and then a real-life problem.

Keywords

Multi-period planning Petrol station replenishment Tank-trucks scheduling and routing Periodicity and frequency service choice 

Notes

Acknowledgements

The authors would like to acknowledge the financial support from Sultan Qaboos University through the internal Grant IG/ENG/MIED/14/04. Moreover, the work of the second author has been partially carried out during his research visit to the University of Tsukuba (Japan) under the Matsumae International Foundation (MIF) fellowship program. The author would like to thank both the MIF and the University of Tsukuba for such opportunity.

References

  1. Archetti, C., Fernández, E., & Huerta-Muñoz, D. L. (2017). The flexible periodic vehicle routing problem. Computers & Operations Research, 85, 58–70.CrossRefGoogle Scholar
  2. Athanasopoulos, T., & Minis, I. (2013). Efficient techniques for the multi-period vehicle routing problem with time windows within a branch and price framework. Annals of Operations Research, 206, 1–22.CrossRefGoogle Scholar
  3. Attanasio, A., Fuduli, A., Ghiani, G., & Triki, T. (2007). Integrating shipment dispatching and packing problems: A case study. Journal of Modelling and Algorithms, 6(1), 77–85.CrossRefGoogle Scholar
  4. Avella, P., Boccia, M., & Sforza, A. (2004). Solving a fuel delivery problem by heuristic and exact approaches. European Journal of Operational Research, 152, 170–179.CrossRefGoogle Scholar
  5. Baldacci, R., Toth, P., & Vigo, D. (2010). Exact algorithms for routing problems under vehicle capacity constraints. Annals of Operations Research, 175, 213–245.CrossRefGoogle Scholar
  6. Baptiste, S., Oliviera, R. C., & Zúquete, E. (2002). A period vehicle routing case study. European Journal of Operational Research, 139, 220–229.CrossRefGoogle Scholar
  7. Barber, K. S., Liu, T. H., Goel, A., & Ramaswamy, S. (1999). Flexible reasoning using sensible agent-based systems: A case study in job flow scheduling. Production Planning and Control, 10(7), 606–615.CrossRefGoogle Scholar
  8. Barbucha, D. (2014). A cooperative population learning algorithm for vehicle routing problem with time windows. Neurocomputing, 146, 210–229.CrossRefGoogle Scholar
  9. Ben Abdelaziz, F., Roucairol, C., & Bacha, C. (2002). Deliveries of liquid fuels to SNDP gas stations using vehicles with multiple compartments. In System management and cyber IEEE international conference, Hammamet, Tunisia.Google Scholar
  10. Beraldi, P., Musmanno, R., & Triki, C. (2000). Solving stochastic linear programs with restricted recourse using interior point methods. Computational Optimization & Applications, 15(3), 215–234.CrossRefGoogle Scholar
  11. Boctor, F., Renaud, J., & Cornillier, F. (2011). Trip packing in petrol stations replenishment. Omega, 39, 86–98.CrossRefGoogle Scholar
  12. Brown, G., Ellis, C. J., Graves, G. W., & Ronen, D. (1987). Real-time wide area dispatch of Mobil tank trucks. Interfaces, 17(1), 107–120.CrossRefGoogle Scholar
  13. Brown, G. G., & Graves, G. W. (1981). Real-time dispatch of petroleum tank trucks. Management Science, 27, 19–32.CrossRefGoogle Scholar
  14. Campbell, A. M., & Wilson, J. H. (2014). Forty years of periodic vehicle routing. Networks, 63(1), 2–15.CrossRefGoogle Scholar
  15. Chao, I.-M., Golden, B. L., & Wasil, E. (1995). A new heuristic for the period traveling salesman problem. Computers & Operations Research, 22, 553–565.CrossRefGoogle Scholar
  16. Christofides, N., & Beasley, J. E. (1984). The period routing problem. Networks, 14, 237–256.CrossRefGoogle Scholar
  17. Cordeau, J. F., Gendreau, M., & Laporte, G. (1997). A tabu search heuristic for periodic and multi-depot vehicle routing problems. Networks, 30, 105–119.CrossRefGoogle Scholar
  18. Cornillier, F., Boctor, F., Laporte, G., & Renaud, J. (2008). A heuristic for the multi-period petrol station replenishment problem. European Journal of Operational Research, 191, 295–305.CrossRefGoogle Scholar
  19. Cornillier, F., Boctor, F., & Renaud, J. (2012). Heuristics for the multi-depot petrol station replenishment problem with time windows. European Journal of Operational Research, 220, 361–369.CrossRefGoogle Scholar
  20. Cornillier, F., Laporte, G., Boctor, F., & Renaud, J. (2009). The petrol station replenishment problem with time windows. Computers & Operations Research, 36, 919–935.CrossRefGoogle Scholar
  21. De Oliveira, F. B., Enayatifar, R., Sadaei, H. J., Guimarães, F. G., & Potvin, J.-Y. (2016). A cooperative coevolutionary algorithm for the multi-depot vehicle routing problem. Expert Systems with Applications, 43, 117–130.CrossRefGoogle Scholar
  22. Diabat, A., Abdallah, T., & Le, T. (2016). A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods. Annals of Operations Research, 242, 373–398.CrossRefGoogle Scholar
  23. Francis, P., Smilowitz, K., & Tzur, M. (2006). The period vehicle routing problem with service choice. Transportation Science, 40(4), 439–454.CrossRefGoogle Scholar
  24. Fu, L. L., Aloulou, M. A., & Triki, C. (2017). Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows. International Journal of Production Research, 55(20), 5942–5957.CrossRefGoogle Scholar
  25. Huang, C. F., Bieniawski, S., Wolpert, D. H., & Strauss, C. E. M. (2005). A comparative study of probability collective based multi-agent systems and genetic algorithms. In Proceedings of the conference on genetic and evolutionary computing (pp. 751–752).Google Scholar
  26. Malépart, V., Boctor, F., Renaud, J., & Labilois, S. (2003). Nouvelles approches pour l’approvisionnement des stations d’essence. Revue Franaise de Gestion Industrielle, 22, 15–31.Google Scholar
  27. Martin, S., Ouelhadj, D., Beullens, P., Ozcan, E., Juan, A. A., & Burke, E. K. (2016). A multi-agent based cooperative approach to scheduling and routing. European Journal of Operational Research, 254(1), 169–178.CrossRefGoogle Scholar
  28. Matei, O., Pop, P. C., Sas, J. L., & Chira, C. (2015). An improved immigration memetic algorithm for solving the heterogeneous fixed fleet vehicle routing problem. Neuro-computing, 150, 58–66.Google Scholar
  29. Morris, P. (1993). The breakout method for escaping from local minima. In Proceedings of the 11th national conference on artificial intelligence (AAAI-93) (pp. 40–45). AAI Press/MIT Press.Google Scholar
  30. Newman, A. M., Yano, C. A., & Kaminsky, P. M. (2005). Third party logistics planning with routing and inventory costs. In J. Geunes & P. M. Pardalos (Eds.), Supply chain optimization (pp. 87–122). New York: Springer.CrossRefGoogle Scholar
  31. Ng, W. L., Leung, S. H., Lam, J. P., & Pan, S. W. (2008). Petrol delivery tanker assignment and routing: A case study in Hong Kong. Journal of the Operations Research Society, 59, 1191–1200.CrossRefGoogle Scholar
  32. Paletta, G., & Triki, C. (2004). Solving the asymmetric traveling salesman problem with periodic constraints. Networks, 44, 31–37.CrossRefGoogle Scholar
  33. Pardalos, P. M., & Romeijn, H. E. (2002). Handbook of global optimization (Vol. 2). Dordrecht, Boston, MA: Kluwer Academic Puplishers.CrossRefGoogle Scholar
  34. Rizzoli, A., Casagrande, N., Donati, A., Gambardella, L., Lepori, D., Montemanni, R., Pina, P., & Zaffalon, M. (2003). Planning and optimization of vehicle routes for fuel oil distribution. In MODSIM international conference on modelling and simulation. Townsville, Australia.Google Scholar
  35. Rothenbächer, A. K. (2017). Branch-and-price-and-cut for the periodic vehicle routing problem with flexible schedule structures. Johannes Gutenberg University Mainz, Discussion paper number 1714. http://www.macro.economics.uni-mainz.de/RePEc/pdf/Discussion_Paper_1714.pdf. Accessed 1 Dec 2018.
  36. Surjandari, I., Rachman, A., Dianawati, F., & Wibowo, R. P. (2011). Petrol delivery assignment with multi-product, multi-depot, split deliveries and time windows. International Journal of Modelling and Optimization, 1(5), 375–379.CrossRefGoogle Scholar
  37. Tan, C. C. R., & Beasley, J. E. (1984). A heuristic algorithm for the period vehicle routing problem. Omega, 12, 497–504.CrossRefGoogle Scholar
  38. Taqa Allah, D., Renaud, J., & Boctor, F. F. (2000). Le probleme d’approvisionnement des stations d’essence. APII-JESA Journal Europeen des Systemes Automatises, 34, 11–33.Google Scholar
  39. Triki, C. (2013). Solution methods for the periodic petrol replenishment problem. The Journal of Engineering Research, 10(2), 69–77.CrossRefGoogle Scholar
  40. Triki, C., & Al-Hinai, N. (2016). Optimisation techniques for planning the petrol replenishment to retail stations over a multi-period horizon. International Journal of Operational Research, 27(1/2), 341–355.CrossRefGoogle Scholar
  41. Triki, C., Al-Hinai, N., Kaabachi, I., & Krichen, S. (2016). An optimization framework for combining the petroleum replenishment problem with the optimal bidding in combinatorial auctions. International Journal of Supply and Operations Management, 3(2), 1318–1331.Google Scholar
  42. Wong, W. S., & Morris, R. J. (1989). A new approach to choosing initial points in local search. Information Processing Letters, 30, 67–72.CrossRefGoogle Scholar
  43. Zhong, W., Liu, J., Xue, M., & Jiao, L. (2004). A multi-agent genetic algorithm for global numerical optimization. IEEE Transactions on Systems, Man, and Cybernetics—Part b: Cybernetics, 34(2), 1128–1141.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial EngineeringSultan Qaboos UniversityMuscatOman
  2. 2.Department of Innovation for EngineeringUniversity of SalentoLecceItaly

Personalised recommendations