Abstract
This work compares the transportation costs incurred by three alternative strategies for shipping items from a central warehouse to a set of customers and vice versa. Two-dimensional loading patterns have to be determined for the transported items. The vehicle routing problem (VRP) with simultaneous pick-ups and deliveries and two-dimensional loading constraints, which considers that vehicles offer simultaneous pick-up and delivery service, is used as the basis for comparisons. Two alternative strategies are considered: the VRP with backhauls and two-dimensional loading constraints, where pick-up items are collected only when the delivery items of a route have been unloaded, and the bi-directional VRP with two-dimensional loading constraints, where pick-up and delivery items are transported by different types of vehicle trips. The examined models are solved via a common local-search method for the routing aspects, integrated with a packing heuristic for developing feasible item loadings. To conduct the model comparison, we solve new benchmark instances with diverse features in terms of the graphs, the characteristics of the transported items, and the participation of pick-up items in the overall set of transported items. Discussion is provided on the routing costs incurred by each transportation model and the behavior of the employed methodology.
Similar content being viewed by others
References
Bortfeldt A (2012) A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints. Comput Oper Res 39(2010):2248–2257. doi:10.1016/j.cor.2011.11.008
Côté J-F, Gendreau M, Potvin J-Y (2014) An exact algorithm for the two-dimensional orthogonal packing problem with unloading constraints. Oper Res 62:1126–1141. doi:10.1287/opre.2014.1307
Crainic TG, Perboli G, Tadei R (2008) Extreme point-based heuristics for three- dimensional bin packing. INFORMS J Comput 20:368–384. doi:10.1287/ijoc.1070.0250
Fekete S, Schepers J, van der Veen JC (2007) An exact algorithm for higher-dimensional orthogonal packing. Oper Res 55:569–587. doi:10.1287/opre.1060.0369
Fuellerer G, Doerner KF, Hartl RF, Iori M (2009) Ant colony optimization for the two-dimensional loading vehicle routing problem. Comput Oper Res 36:655–673. doi:10.1016/j.cor.2007.10.021
Fuellerer G, Doerner KF, Hartl RF, Iori M (2010) Metaheuristics for vehicle routing problems with three-dimensional loading constraints. Eur J Oper Res 201:751–759. doi:10.1016/j.ejor.2009.03.046
Gendreau M, Iori M, Laporte G, Martello S (2006) A tabu search algorithm for a routing and container loading problem. Transp Sci 40:342–350. doi:10.1287/trsc.1050.0145
Gendreau M, Iori M, Laporte G, Martello S (2008) A tabu search heuristic for the vehicle routing problem with two-dimensional loading constraints. Networks 51:514–518. doi:10.1002/net.20192
Iori M, Martello S (2010) Routing problems with loading constraints. TOP 18:4–27. doi:10.1007/s11750-010-0144-x
Iori M, Martello S (2013) An annotated bibliography of combined routing and loading problems. Yugosl J Oper Res 23:311–326
Iori M, Salazar-Gonzãlez J-J, Vigo D (2007) An exact approach for the vehicle routing problem with two-dimensional loading constraints. Transp Sci 41:253–264. doi:10.1287/trsc.1060.0165
Laporte G (2009) Fifty years of vehicle routing. Transp Sci 43:408–416. doi:10.1287/trsc.1090.0301
Leung SCH, Zhou X, Zhang D, Zheng J (2011) Extended guided tabu search and a new packing algorithm for the two-dimensional loading vehicle routing problem. Comput Oper Res 38:205–215. doi:10.1016/j.cor.2010.04.013
Lodi A, Martello S, Vigo D (1999) Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems. INFORMS J Comput 11:345–357. doi:10.1287/ijoc.11.4.345
Martello S, Pisinger D, Vigo D (2000) The three-dimensional bin packing problem. Oper Res 48:256–267. doi:10.1287/opre.48.2.256.12386
Perboli G, Gobbato L, Perfetti F (2014) Packing problems in transportation and supply chain: new problems and trends. Procedia Social Behav Sci 111:672–681. doi:10.1016/j.sbspro.2014.01.101
Tao Y, Wang F (2015) An effective tabu search approach with improved loading algorithms for the 3L-CVRP. Comput Oper Res 55:127–140. doi:10.1016/j.cor.2013.10.017
Tarantilis CD, Zachariadis EE, Kiranoudis CT (2009) A hybrid metaheuristic algorithm for the integrated vehicle routing and three-dimensional container-loading problem. IEEE Trans Intell Transp Syst 10:255–271. doi:10.1109/TITS.2009.2020187
Whittley IM, Smith GD (2004) The attribute based hill climber. J Math Model Algorithms 3:167–178. doi:10.1023/B:JMMA.0000036583.17284.02
Zachariadis EE, Kiranoudis CT (2010) A strategy for reducing the computational complexity of local search-based methods for the vehicle routing problem. Comput Oper Res 37:2089–2105. doi:10.1016/j.cor.2010.02.009
Zachariadis EE, Tarantilis CD, Kiranoudis CT (2012) The pallet-packing vehicle routing problem. Transp Sci 46:341–358. doi:10.1287/trsc.1110.0373
Zachariadis EE, Tarantilis CD, Kiranoudis CT (2013) Integrated distribution and loading planning via a compact metaheuristic algorithm. Eur J Oper Res 228:56–71. doi:10.1016/j.ejor.2013.01.040
Zachariadis EE, Tarantilis CD, Kiranoudis CT (2015) The vehicle routing problem with simultaneous pick-ups and deliveries and two-dimensional loading constraints. Eur J Oper Res. doi:10.1016/j.ejor.2015.11.018
Zhu W, Qin H, Lim A, Wang L (2012) A two-stage tabu search algorithm with enhanced packing heuristics for the 3L-CVRP and M3L-CVRP. Comput Oper Res 39:2178–2195. doi:10.1016/j.cor.2011.11.001
Acknowledgments
The work presented in this paper was supported by ΙΚY fellowships of excellence for postgraduate studies in Greece – Siemens program. The authors would like to thank the two anonymous referees and the editor for their valuable remarks that improved the manuscript.
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Zachariadis, E.E., Tarantilis, C.D. & Kiranoudis, C.T. Vehicle routing strategies for pick-up and delivery service under two dimensional loading constraints. Oper Res Int J 17, 115–143 (2017). https://doi.org/10.1007/s12351-015-0218-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12351-015-0218-5