Abstract
This paper deals with a special vehicle routing problem with backhauls where customers may want to receive items from a depot and, at the same time, return items back to the depot. Moreover, time windows are assumed and three-dimensional loading constraints are to be observed, i.e. the items are three-dimensional boxes and packing constraints, e.g. regarding load stability, are to be met. The resulting problem is the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), time windows and three-dimensional loading constraints (3L-VRPSDPTW). This problem occurs, for example, if retail stores are supplied by a central warehouse and wish to return packaging material. A particular challenge of the problem consists of transporting delivery and pickup items simultaneously on the same vehicle. In order to avoid any reloading effort during a tour, we consider two different approaches for loading the vehicles: (i) loading from the back with separation of the loading space into a delivery section and a pickup section and (ii) loading from the (long) side. A hybrid algorithm is proposed for the 3L-VRPSDPTW consisting of an adaptive large neighbourhood search for the routing and different packing heuristics for the loading part of the problem. Extensive numerical experiments are conducted with VRPSDP instances from the literature and newly generated instances for the 3L-VRPSDPTW.
Similar content being viewed by others
Notes
Note that we omit the 14 instances with drop times and maximum distance constraints since those problem aspects are not considered here and the instances are identical to the other 14 instances with respect to the other problem information.
Computer used by Gonçalves and Resende (2012): AMD 2.2 GHz Opteron 6-core CPU with Linux (Fedora release 12) operating system.
References
Angelelli E, Mansini R (2002) The vehicle routing problem with time windows and simultaneous pick-up and delivery. In: Klose A, Speranza MG, van Wassenhove LN (eds) Quantitative approaches to distribution logistics and supply chain management. Springer, Berlin, pp 249–267. https://doi.org/10.1007/978-3-642-56183-2_15
Avci M, Topaloglu S (2016) A hybrid metaheuristic algorithm for heterogeneous vehicle routing problem with simultaneous pickup and delivery. Expert Syst Appl 53:160–171. https://doi.org/10.1016/j.eswa.2016.01.038
Baker BS, Coffman EG Jr, Rivest RL (1980) Orthogonal packings in two dimensions. SIAM J Comput 9(4):846–855. https://doi.org/10.1137/0209064
Baldacci R, Mingozzi A, Roberti R (2011) New route relaxation and pricing strategies for the vehicle routing problem. Oper Res 59(5):1269–1283. https://doi.org/10.1287/opre.1110.0975
Bartók T, Imreh C (2011) Pickup and delivery vehicle routing with multidimensional loading constraints. Acta Cybern 20(1):17–33. https://doi.org/10.14232/actacyb.20.1.2011.3
Bischoff EE, Ratcliff M (1995) Issues in the development of approaches to container loading. Omega 23(4):377–390. https://doi.org/10.1016/0305-0483(95)00015-G
Bortfeldt A (2012) A hybrid algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints. Comput Oper Res 39(9):2248–2257. https://doi.org/10.1016/j.cor.2011.11.008
Bortfeldt A, Hahn T, Männel D, Mönch L (2015) Hybrid algorithms for the vehicle routing problem with clustered backhauls and 3D loading constraints. Eur J Oper Res 243(1):82–96. https://doi.org/10.1016/j.ejor.2014.12.001
Brandão J (2006) A new tabu search algorithm for the vehicle routing problem with backhauls. Eur J Oper Res 173(2):540–555. https://doi.org/10.1016/j.ejor.2005.01.042
Çatay B (2010) A new saving-based ant algorithm for the vehicle routing problem with simultaneous pickup and delivery. Expert Syst Appl 37(10):6809–6817. https://doi.org/10.1016/j.eswa.2010.03.045
Chabrier A (2006) Vehicle routing problem with elementary shortest path based column generation. Comput Oper Res 33(10):2972–2990. https://doi.org/10.1016/j.cor.2005.02.029
Clarke G, Wright JW (1964) Scheduling of vehicles from a central depot to a number of delivery points. Oper Res 12(4):568–581. http://www.jstor.org/stable/167703
Cook W, Rich JL (1999) A parallel cutting-plane algorithm for the vehicle routing problem with time windows. Computational and Applied Mathematics Department, Rice University, Houston, TX, Technical Report
Crispim J, Brandão J (2005) Metaheuristics applied to mixed and simultaneous extensions of vehicle routing problems with backhauls. J Oper Res Soc 56(11):1296–1302. http://www.jstor.org/stable/4102082
Davies A, Bischoff EE (1999) Weight distribution considerations in container loading. Eur J Oper Res 114(3):509–527. https://doi.org/10.1016/S0377-2217(98)00139-8
Dell’Amico M, Righini G, Salani M (2006) A branch-and-price approach to the vehicle routing problem with simultaneous distribution and collection. Transp Sci 40(2):235–247. https://doi.org/10.1287/trsc.1050.0118
Demir E, Bektaş T, Laporte G (2012) An adaptive large neighborhood search heuristic for the pollution-routing problem. Eur J Oper Res 223(2):346–359. https://doi.org/10.1016/j.ejor.2012.06.044
Desaulniers G, Lessard F, Hadjar A (2008) Tabu search, partial elementarity, and generalized k -path inequalities for the vehicle routing problem with time windows. Transp Sci 42(3):387–404. https://doi.org/10.1287/trsc.1070.0223
Dethloff J (2001) Vehicle routing and reverse logistics: the vehicle routing problem with simultaneous delivery and pick-up. OR Spektrum 23(1):79–96. https://doi.org/10.1007/PL00013346
Dominguez O, Guimarans D, Juan AA (2015) A hybrid heuristic for the 2L-VRP with clustered backhauls. In: Proceedings of the XVI Conferencia de la Asociación Española para la Inteligencia Artificial (CAEPIA)
Fan J (2011) The vehicle routing problem with simultaneous pickup and delivery based on customer satisfaction. Procedia Eng 15:5284–5289. https://doi.org/10.1016/j.proeng.2011.08.979
Fuellerer G, Doerner KF, Hartl RF, Iori M (2010) Metaheuristics for vehicle routing problems with three-dimensional loading constraints. Eur J Oper Res 201(3):751–759. https://doi.org/10.1016/j.ejor.2009.03.046
Gajpal Y, Abad PL (2009) Multi-ant colony system (MACS) for a vehicle routing problem with backhauls. Eur J Oper Res 196(1):102–117. https://doi.org/10.1016/j.ejor.2008.02.025
García-Nájera A, Bullinaria JA, Gutiérrez-Andrade MA (2015) An evolutionary approach for multi-objective vehicle routing problems with backhauls. Comput Ind Eng 81:90–108. https://doi.org/10.1016/j.cie.2014.12.029
Gélinas S, Desrochers M, Desrosiers J, Solomon MM (1995) A new branching strategy for time constrained routing problems with application to backhauling. Ann Oper Res 61(1):91–109. https://doi.org/10.1007/BF02098283
Gendreau M, Iori M, Laporte G, Martello S (2006) A tabu search algorithm for a routing and container loading problem. Transp Sci 40(3):342–350. https://doi.org/10.1287/trsc.1050.0145
Goetschalckx M, Jacobs-Blecha C (1989) The vehicle routing problem with backhauls. Eur J Oper Res 42(1):39–51. https://doi.org/10.1016/0377-2217(89)90057-X
Gonçalves JF, Resende MG (2012) A parallel multi-population biased random-key genetic algorithm for a container loading problem. Comput Oper Res 39(2):179–190. https://doi.org/10.1016/j.cor.2011.03.009
Halse K (1992) Modeling and solving complex vehicle routing problems. Ph.D. Thesis, Technical University of Denmark, Lyngby
Hopper E (2000) Two-dimensional packing utilising evolutionary algorithms and other meta-heuristic methods. Ph.D. Thesis, University of Wales. Cardiff
Iori M, Martello S (2010) Routing problems with loading constraints. TOP 18(1):4–27. https://doi.org/10.1007/s11750-010-0144-x
Irnich S, Villeneuve D (2006) The shortest-path problem with resource constraints and k -cycle elimination for k \(\ge \) 3. INFORMS J Comput 18(3):391–406. https://doi.org/10.1287/ijoc.1040.0117
Irnich S, Toth P, Vigo D (2014) The family of vehicle routing problems. In: Toth P, Vigo D (eds) Vehicle routing, MOS-SIAM series on optimization. SIAM, Philadelphia, pp 1–33
Jakobs S (1996) On genetic algorithms for the packing of polygons. Eur J Oper Res 88(1):165–181. https://doi.org/10.1016/0377-2217(94)00166-9
Jepsen M, Petersen B, Spoorendonk S, Pisinger D (2008) Subset-row inequalities applied to the vehicle-routing problem with time windows. Oper Res 56(2):497–511. https://doi.org/10.1287/opre.1070.0449
Jun Y, Kim BI (2012) New best solutions to VRPSPD benchmark problems by a perturbation based algorithm. Expert Syst Appl 39(5):5641–5648. https://doi.org/10.1016/j.eswa.2011.11.053
Kallehauge B, Larsen J, Madsen OB (2000) Lagrangian duality and non-differentiable optimization applied on routing with time windows-experimental results. Relatório interno IMM-REP-2000-8, Department of Mathematical Modeling, Technical University of Denmark, Lyngby, Dinamarca
Karabulut K, Inceoglu MM (2005) A hybrid genetic algorithm for packing in 3D with deepest bottom left with fill method. In: Yakhno T (ed) Advances in information systems. Lecture Notes in Computer Science, vol 3261. Springer, Berlin, pp 441–450. https://doi.org/10.1007/978-3-540-30198-1_45
Kohl N, Desrosiers J, Madsen OBG, Solomon MM, Soumis F (1999) 2-Path cuts for the vehicle routing problem with time windows. Transp Sci 33(1):101–116. https://doi.org/10.1287/trsc.33.1.101
Larsen J (1999) Parallelization of the vehicle routing problem with time windows. Ph.D. Thesis, Technical University of Denmark, Department of Informatics and Mathematical Modeling
Liu D, Teng H (1999) An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles. Eur J Oper Res 112(2):413–420. https://doi.org/10.1016/S0377-2217(97)00437-2
Lodi A, Martello S, Vigo D (1999) Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems. INFORMS J Comput 11(4):345–357. https://doi.org/10.1287/ijoc.11.4.345
Ma Hw, Zhu W, Xu S (2011) Research on the algorithm for 3L-CVRP with considering the utilization rate of vehicles. In: Chen R (ed) Intelligent computing and information science, communications in computer and information science, vol 134. Springer, Berlin, pp 621–629. https://doi.org/10.1007/978-3-642-18129-0_94
Männel D, Bortfeldt A (2016) A hybrid algorithm for the vehicle routing problem with pickup and delivery and three-dimensional loading constraints. Eur J Oper Res 254(3):840–858. https://doi.org/10.1016/j.ejor.2016.04.016
Maquera G, Laguna M, Gandelman DA, Sant’Anna AP (2012) Scatter search applied to the vehicle routing problem with simultaneous delivery and pickup. In: Yin PY (ed) Trends in developing metaheuristics, algorithms, and optimization approaches. IGI Global, pp 149–168. https://doi.org/10.4018/978-1-4666-2145-9.ch010
Mester D, Bräysy O, Dullaert W (2007) A multi-parametric evolution strategies algorithm for vehicle routing problems. Expert Syst Appl 32(2):508–517. https://doi.org/10.1016/j.eswa.2005.12.014
Miao L, Ruan Q, Woghiren K, Ruo Q (2012) A hybrid genetic algorithm for the vehicle routing problem with three-dimensional loading constraints. RAIRO Oper Res 46(1):63–82. https://doi.org/10.1051/ro/2012008
Min H (1989) The multiple vehicle routing problem with simultaneous delivery and pick-up points. Transp Res Part A Gen 23(5):377–386. https://doi.org/10.1016/0191-2607(89)90085-X
Moura A (2008) A multi-objective genetic algorithm for the vehicle routing with time windows and loading problem. In: Bortfeldt A, Homberger J, Kopfer H, Pankratz G, Strangmeier R (eds) Intelligent decision support, Gabler Edition Wissenschaft, Betriebswirtschaftlicher Verlag Dr. Th. Gabler/GWV Fachverlage GmbH Wiesbaden, Wiesbaden, pp 187–201. https://doi.org/10.1007/978-3-8349-9777-7_11
Moura A, Oliveira JF (2009) An integrated approach to the vehicle routing and container loading problems. OR Spectr 31(4):775–800. https://doi.org/10.1007/s00291-008-0129-4
Osman IH, Wassan NA (2002) A reactive tabu search meta-heuristic for the vehicle routing problem with back-hauls. J Sched 5(4):263–285. https://doi.org/10.1002/jos.122
Parragh SN, Doerner KF, Hartl RF (2008) A survey on pickup and delivery problems. Journal für Betriebswirtschaft 58(1):21–51. https://doi.org/10.1007/s11301-008-0033-7
Pinto T, Alves C, De C, Moura A (2015) An insertion heuristic for the capacitated vehicle routing problem with loading constraints and mixed linehauls and backhauls. FME Trans 43(4):311–318. https://doi.org/10.5937/fmet1504311P
Polat O, Kalayci CB, Kulak O, Günther HO (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(2):369–382. https://doi.org/10.1016/j.ejor.2014.10.010
Pollaris H, Braekers K, Caris A, Janssens GK, Limbourg S (2015) Vehicle routing problems with loading constraints: state-of-the-art and future directions. OR Spectr 37(2):297–330. https://doi.org/10.1007/s00291-014-0386-3
Potvin JY, Duhamel C, Guertin F (1996) A genetic algorithm for vehicle routing with backhauling. Appl Intell 6(4):345–355. https://doi.org/10.1007/BF00132738
Reimann M, Doerner K, Hartl RF (2002) Insertion based ants for vehicle routing problems with backhauls and time windows. In: Dorigo M, Di Caro G, Sampels M (eds) Ant algorithms: third international workshop, ANTS 2002 Brussels, Belgium, September 12–14, 2002 Proceedings, Springer, Berlin, pp 135–148. https://doi.org/10.1007/3-540-45724-0_12
Rieck J, Zimmermann J (2013) Exact solutions to the symmetric and asymmetric vehicle routing problem with simultaneous delivery and pick-up. Bus Res 6(1):77–92. https://doi.org/10.1007/BF03342743
Ropke S, Pisinger D (2006) A unified heuristic for a large class of vehicle routing problems with backhauls. Eur J Oper Res 171(3):750–775. https://doi.org/10.1016/j.ejor.2004.09.004
Ropke S, Pisinger D (2006) An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transp Sci 40(4):455–472. https://doi.org/10.1287/trsc.1050.0135
Salani M (2006) Branch-and-price algorithms for vehicle routing problems. Ph.D. Thesis, Università degli studi di Milano
Salhi S, Nagy G (1999) A cluster insertion heuristic for single and multiple depot vehicle routing problems with backhauling. J Oper Res Soc 50(10):1034. https://doi.org/10.2307/3009928
Shaw P (1997) A new local search algorithm providing high quality solutions to vehicle routing problems
Shaw P (1998) Using constraint programming and local search methods to solve vehicle routing problems. In: Maher M, Puget JF (eds) Principles and practice of constraint programming—CP98. Lecture Notes in Computer Science, vol 1520. Springer, Berlin, pp 417–431. https://doi.org/10.1007/3-540-49481-2_30
Solomon MM (1987) Algorithms for the vehicle routing and scheduling problems with time window constraints. Oper Res 35(2):254–265
Subramanian A, Drummond L, Bentes C, Ochi LS, Farias R (2010) A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery. Comput Oper Res 37(11):1899–1911. https://doi.org/10.1016/j.cor.2009.10.011
Subramanian A, Uchoa E, Ochi LS (2010) New lower bounds for the vehicle routing problem with simultaneous pickup and delivery. In: Festa P (ed) Experimental algorithms. Lecture Notes in Computer Science, vol 6049. Springer, Berlin, pp 276–287. https://doi.org/10.1007/978-3-642-13193-6_24
Subramanian A, Uchoa E, Pessoa AA, Ochi LS (2013) Branch-cut-and-price for the vehicle routing problem with simultaneous pickup and delivery. Optim Lett 7(7):1569–1581. https://doi.org/10.1007/s11590-012-0570-9
Tang Montané FA, Galvão RD (2006) A tabu search algorithm for the vehicle routing problem with simultaneous pick-up and delivery service. Comput Oper Res 33(3):595–619. https://doi.org/10.1016/j.cor.2004.07.009
Tao Y, Wang F (2015) An effective tabu search approach with improved loading algorithms for the 3L-CVRP. Comput Oper Res 55:127–140. https://doi.org/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(2):255–271. https://doi.org/10.1109/TITS.2009.2020187
Tasan AS, Gen M (2012) A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries. Comput Ind Eng 62(3):755–761. https://doi.org/10.1016/j.cie.2011.11.025
Toth P, Vigo D (1996) A heuristic algorithm for the vehicle routing problem with backhauls. In: Bianco L, Toth P (eds) Advanced methods in transportation analysis. Springer, Berlin, pp 585–608. https://doi.org/10.1007/978-3-642-85256-5_26
Toth P, Vigo D (1997) An exact algorithm for the vehicle routing problem with backhauls. Transp Sci 31(4):372–385. https://doi.org/10.1287/trsc.31.4.372
Wang C, Mu D, Zhao F, Sutherland JW (2015) A parallel simulated annealing method for the vehicle routing problem with simultaneous pickup-delivery and time windows. Comput Ind Eng 83:111–122. https://doi.org/10.1016/j.cie.2015.02.005
Wang HF, Chen YY (2012) A genetic algorithm for the simultaneous delivery and pickup problems with time window. Comput Ind Eng 62(1):84–95. https://doi.org/10.1016/j.cie.2011.08.018
Wang L, Guo S, Chen S, Zhu W, Lim A (2010) Two natural heuristics for 3D packing with practical loading constraints. In: Zhang BT, Orgun MA (eds) PRICAI 2010: trends in artificial intelligence. Lecture Notes in Computer Science, Lecture Notes in Artificial Intelligence, vol 6230. Springer, Berlin, pp 256–267. https://doi.org/10.1007/978-3-642-15246-7_25
Wassan NA, Nagy G, Ahmadi S (2008) A heuristic method for the vehicle routing problem with mixed deliveries and pickups. J Sched 11(2):149–161. https://doi.org/10.1007/s10951-008-0055-y
Wassan NA, Wassan AH, Nagy G (2008) A reactive tabu search algorithm for the vehicle routing problem with simultaneous pickups and deliveries. J Comb Optim 15(4):368–386. https://doi.org/10.1007/s10878-007-9090-4
Wei L, Zhang Z, Lim A (2014) An adaptive variable neighborhood search for a heterogeneous fleet vehicle routing problem with three-dimensional loading constraints. IEEE Comput Intell Mag 9(4):18–30. https://doi.org/10.1109/MCI.2014.2350933
Wisniewski MA, Ritt M, Buriol LS (2011) A tabu search algorithm for the capacitated vehicle routing problem with three-dimensional loading constraints. In: XLIII Simposio Brasilero de Pesquisa Operacional
Zachariadis EE, Tarantilis CD, Kiranoudis CT (2009) A hybrid metaheuristic algorithm for the vehicle routing problem with simultaneous delivery and pick-up service. Expert Syst Appl 36(2):1070–1081. https://doi.org/10.1016/j.eswa.2007.11.005
Zachariadis EE, Tarantilis CD, Kiranoudis CT (2010) An adaptive memory methodology for the vehicle routing problem with simultaneous pick-ups and deliveries. Eur J Oper Res 202(2):401–411. https://doi.org/10.1016/j.ejor.2009.05.015
Zachariadis EE, Tarantilis CD, Kiranoudis CT (2016) The vehicle routing problem with simultaneous pick-ups and deliveries and two-dimensional loading constraints. Eur J Oper Res 251(2):369–386. https://doi.org/10.1016/j.ejor.2015.11.018
Zhang T, Chaovalitwongse WA, Zhang Y (2012) Scatter search for the stochastic travel-time vehicle routing problem with simultaneous pick-ups and deliveries. Comput Oper Res 39(10):2277–2290. https://doi.org/10.1016/j.cor.2011.11.021
Zhang T, Chaovalitwongse WA, Zhang Y (2014) Integrated ant colony and tabu search approach for time dependent vehicle routing problems with simultaneous pickup and delivery. J Comb Optim 28(1):288–309. https://doi.org/10.1007/s10878-014-9741-1
Zhang Z, Wei L, Lim A (2015) An evolutionary local search for the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints. Transp Res Part B Methodol 82:20–35. https://doi.org/10.1016/j.trb.2015.10.001
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(9):2178–2195. https://doi.org/10.1016/j.cor.2011.11.001
Acknowledgements
We thank Lijun Wei (JiangXi University of Finance and Economics, Nanchang, China) for providing us with the programme for the local search and the open space heuristic.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Koch, H., Bortfeldt, A. & Wäscher, G. A hybrid algorithm for the vehicle routing problem with backhauls, time windows and three-dimensional loading constraints. OR Spectrum 40, 1029–1075 (2018). https://doi.org/10.1007/s00291-018-0506-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00291-018-0506-6