Advertisement

Annals of Operations Research

, Volume 275, Issue 2, pp 321–338 | Cite as

A branch-and-cut algorithm for the multi-compartment vehicle routing problem with flexible compartment sizes

  • Tino HenkeEmail author
  • M. Grazia Speranza
  • Gerhard Wäscher
Original Research
  • 73 Downloads

Abstract

Multi-compartment vehicle routing problems arise in a variety of problem settings in which different product types have to be transported separated from each other. In this paper, a problem variant which occurs in the context of glass waste recycling is considered. In this problem, a set of locations exists, each of which offering a number of containers for the collection of different types of glass waste (e.g. colorless, green, brown glass). In order to pick up the contents from the containers, a fleet of homogeneous disposal vehicles is available. Individually for each disposal vehicle, the capacity can be discretely separated into a limited number of compartments to which different glass waste types are assigned. The objective of the problem is to minimize the total distance to be travelled by the disposal vehicles. For solving this problem to optimality, a branch-and-cut algorithm has been developed and implemented. Extensive numerical experiments have been conducted in order to evaluate the algorithm and to gain insights into the problem structure. The corresponding results show that the algorithm is able to solve instances with up to 50 locations to optimality and that it reduces the computing time by 87% compared to instances from the literature. Additional experiments give managerial insights into the use of different variants of compartments with flexible sizes.

Keywords

Vehicle routing Multiple compartments Branch-and-cut algorithm Waste collection 

References

  1. Abdulkader, M. M. S., Gajpal, Y., & El Mekkawy, T. Y. (2015). Hybridized ant colony algorithm for the multi compartment vehicle routing problem. Applied Soft Computing, 37, 196–203.CrossRefGoogle Scholar
  2. Archetti, C., Campbell, A., & Speranza, M. G. (2016). Multi-commodity versus single-commodity routing. Transportation Science, 50, 461–472.CrossRefGoogle Scholar
  3. 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
  4. Brown, G. G., & Graves, G. W. (1981). Real-time dispatch of petroleum tank trucks. Management Science, 27, 19–32.CrossRefGoogle Scholar
  5. Caramia, M., & Guerriero, F. (2010). A milk collection problem with incompatibility constraints. Interfaces, 40, 130–143.CrossRefGoogle Scholar
  6. Chajakis, E. D., & Guignard, M. (2003). Scheduling deliveries in vehicles with multiple compartments. Journal of Global Optimization, 26, 43–78.CrossRefGoogle Scholar
  7. Coelho, L. C., & Laporte, G. (2015). Classification, models and exact algorithms for multi-compartment delivery problems. European Journal of Operational Research, 242, 854–864.CrossRefGoogle Scholar
  8. Cornillier, F., Boctor, F. 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
  9. Cornuejols, G., & Harche, F. (1993). Polyhedral study of the capacitated vehicle routing problem. Mathematical Programming, 60, 21–52.CrossRefGoogle Scholar
  10. Derigs, U., Gottlieb, J., Kalkoff, J., Piesche, M., Rothlauf, F., & Vogel, U. (2011). Vehicle routing with compartments: Applications, modelling and heuristics. OR Spectrum, 33, 885–914.CrossRefGoogle Scholar
  11. El Fallahi, A., Prins, C., & Wolfer Calvo, R. (2008). A memetic algorithm and a tabu search for the multi-compartment vehicle routing problem. Computers & Operations Research, 35, 1725–1741.CrossRefGoogle Scholar
  12. Elbek, M., & Wøhlk, S. (2016). A variable neighborhood search for the multi-period collection of recyclable materials. European Journal of Operational Research, 249, 540–550.CrossRefGoogle Scholar
  13. Fagerholt, K., & Christiansen, M. (2000). A combined ship scheduling and allocation problem. Journal of the Operational Research Society, 51, 834–842.CrossRefGoogle Scholar
  14. Golden, B. L., Raghavan, S., & Wasil, E. A. (2008). The vehicle routing problem: Latest advances and new challenges. New York: Springer.CrossRefGoogle Scholar
  15. Goodson, J. C. (2015). A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands. European Journal of Operational Research, 241, 361–369.CrossRefGoogle Scholar
  16. Henke, T., Speranza, M. G., & Wäscher, G. (2015). The multi-compartment vehicle routing problem with flexible compartment sizes. European Journal of Operational Research, 246, 730–746.CrossRefGoogle Scholar
  17. Koch, H., Henke, T., Wäscher, G. (2016): A genetic algorithm for the multi-compartment vehicle routing problem with flexible compartment sizes. Working Paper No. 04/2016, Fakultät für Wirtschaftswissenschaft, Otto-von-Guericke Universität Magdeburg.Google Scholar
  18. Lahyani, R., Coelho, L. C., Khemakhem, M., Laporte, G., & Semet, F. (2015). A multi-compartment vehicle routing problem arising in the collection of olive oil in Tunisia. Omega, 51, 1–10.CrossRefGoogle Scholar
  19. Laporte, G. (2009). Fifty years of vehicle routing. Transportation Science, 43, 408–416.CrossRefGoogle Scholar
  20. Mendoza, J. E., Castanier, B., Guéret, C., Medaglia, A. L., & Velasco, N. (2010). A memetic algorithm for the multi-compartment vehicle routing problem with stochastic demands. Computers & Operations Research, 37, 1886–1898.CrossRefGoogle Scholar
  21. Mendoza, J. E., Castanier, B., Guéret, C., Medaglia, A. L., & Velasco, N. (2011). Constructive heuristics for the multicompartment vehicle routing problem with stochastic demands. Transportation Science, 45, 346–363.CrossRefGoogle Scholar
  22. Muyldermans, L., & Pang, G. (2010). On the benefits of co-collection: Experiments with a multi-compartment vehicle routing problem. European Journal of Operational Research, 206, 93–103.CrossRefGoogle Scholar
  23. Rabbani, M., Farrokhi-asl, H., & Rafiei, H. (2016). A hybrid genetic algorithm for waste collection problem by heterogeneous fleet of vehicles with multiple separated compartments. Journal of Intelligent & Fuzzy Systems, 30, 1817–1830.CrossRefGoogle Scholar
  24. Ralphs, T. K., Kopman, L., Pulleyblank, W. R., & Trotter, L. E. (2003). On the capacitated vehicle routing problem. Mathematical Programming, Series B, 94, 343–359.CrossRefGoogle Scholar
  25. Reed, M., Yiannakou, A., & Evering, R. (2014). An ant colony algorithm for the multi-compartment vehicle routing problem. Applied Soft Computing, 15, 169–176.CrossRefGoogle Scholar
  26. Toth, P., & Vigo, D. (2014). Vehicle routing: Problems, methods, and applications (2nd ed.). Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
  27. Vidović, M., Popović, D., & Ratković, B. (2014). Mixed integer and heuristics model for the inventory routing problem in fuel delivery. International Journal of Production Economics, 147, 593–604.CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Management ScienceOtto-von-Guericke-University MagdeburgMagdeburgGermany
  2. 2.Department of Quantitative MethodsUniversity of BresciaBresciaItaly
  3. 3.School of Mechanical, Electronic and Control EngineeringBeijing Jiaotong UniversityBeijingChina

Personalised recommendations