Exact |
Iori et al. (2007)IORI M, SALAZAR-GONZÁLEZ JJ & VIGO D. 2007. An exact approach for the vehicle routing problem with two-dimensional loading constraints. Transportation Science , 41(2): 253-264.
|
2L-CVRP |
Sequential |
= |K| |
No |
Integer |
B&C |
Azevedo et al. (2009)AZEVEDO BLP, HOKAMA P, MIYAZAWA FK & XAVIER EC. 2009. A Branch-and-Cut Approach for the Vehicle Routing Problem with Two-dimensional Loading Constraints. In: XLI Simpósio Brasileiro de Pesquisa Operacional. pp. 2491-2502. Brazil.
|
2L-CVRP |
Sequential and Unrestricted |
= |K| |
No |
Integer |
B&C |
Hokama et al. (2016)HOKAMA P, MIYAZAWA FK & XAVIER EC. 2016. A branch-and-cut approach for the vehicle routing problem with loading constraints. Expert Systems with Applications, 47: 1-13.
|
2L-CVRP |
Sequential |
= |K| |
No |
Integer |
B&C |
Côté et al. (2017)CÔTÉ JF, GUASTAROBA G & SPERANZA MG. 2017. The value of integrating loading and routing. European Journal of Operational Research, 257(1): 89-105.
|
2L-CVRP |
Sequential |
≥ |K| |
Yes |
Integer |
B&C |
Heuristics |
Gendreau et al. (2008)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(1): 4-18.
|
2L-CVRP |
Sequential |
= |K| |
No Yes |
Integer Real |
Tabu Search |
Sequential and Unrestricted |
≤ |K| |
Fuellerer et al. (2009)FUELLERER G, DOERNER KF, HARTL RF & IORI M. 2009. Ant colony optimization for the two-dimensional loading vehicle routing problem. Computers & Operations Research , 36(3): 655-673.
|
2L-CVRP |
Sequential |
= |K| |
No Yes |
Integer Real |
Ant Colony Algorithm |
Sequential and Unrestricted |
≤ |K| |
Zachariadis et al. (2009)ZACHARIADIS EE, TARANTILIS CD & KIRANOUDIS CT. 2009. A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints. European Journal of Operational Research , 195(3): 729-743.
|
2L-CVRP |
Sequential and Unrestricted |
≤ |K| |
Yes |
Real |
Guided Tabu Search |
Strodl et al. (2010)STRODL J, DOERNER KF, TRICOIRE F & HARTL RF. 2010. On Index Structures in Hybrid Metaheuristics for Routing Problems with Hard Feasibility Checks: An Application to the 2- Dimensional Loading Vehicle Routing Problem. In: BLESA MJ, BLUM C, RAIDL G, ROLI A & SAMPELS M (Eds.), Proceedings of the 7th International Workshop on Hybrid Metaheuristics, vol. 6373. pp. 160-173. Springer Berlin Heidelberg.
|
2L-CVRP |
Unrestricted |
≤ |K| |
Yes |
Real |
Variable Neighborhood Search |
Leung et al. (2010)LEUNG SCH, ZHENG J, ZHANG D & ZHOU X. 2010. Simulated annealing for the vehicle routing problem with two-dimensional loading constraints. Flexible Services and Manufacturing Journal, 22(1-2): 61-82.
|
2L-CVRP |
Sequential and Unrestricted |
≤ |K| |
Yes |
Real |
Simulated Annealing |
Duhamel et al. (2011)DUHAMEL C, LACOMME P, QUILLIOT A & TOUSSAINT H. 2011. A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem. Computers & Operations Research , 38(3): 617-640.
|
2L-CVRP |
Unrestricted |
≤ |K| |
Yes |
Real |
GRASP |
Leung et al. (2011)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. Computers & Operations Research , 38(1): 205-215.
|
2L-CVRP |
Sequential and Unrestricted |
≤ |K| |
Yes |
Real |
Extended Guided Tabu Search |
Shen & Murata (2012)SHEN Y & MURATA T. 2012. Pick-up Scheduling of Two-dimensional Loading in Vehicle Routing Problem by using GA. In: Proceedings of the 2012 International MultiConference of Engineers and Computer Scientists (IMECS), vol. 2. pp. 1532-1537.
|
2L-CVRP |
Sequential |
≤ |K| |
- |
Real |
Genetic algorithm |
Bin et al. (2013)BIN W, HONG C & ZHI-YONG C. 2013. Artificial bee colony algorithm for two-dimensional loading capacitated vehicle routing problem. In: 2013 International Conference on Management Science and Engineering (ICMSE). pp. 406-412.
|
2L-CVRP |
Sequential and Unrestricted |
≤ |K| |
Yes |
Real |
Artificial Bee Colony |
Zachariadis et al. (2013)ZACHARIADIS EE, TARANTILIS CD & KIRANOUDIS CT. 2013. Integrated distribution and loading planning via a compact metaheuristic algorithm. European Journal of Operational Research , 228(1): 56-71.
|
2L-CVRP |
Sequential and Unrestricted |
≤ |K| |
Yes |
Real |
Local Search |
Domínguez et al. (2014)DOMÍNGUEZ O, JUAN AA & FAULIN J. 2014. A biased-randomized algorithm for the two- dimensional vehicle routing problem with and without item rotations. International Transactions in Operational Research, 21(3): 375-398.
|
2L-CVRP |
Unrestricted |
≤ |K| |
Yes |
Real |
Multistart Biased-Randomized Algorithm |
Wei et al. (2015)WEI L, ZHANG Z, ZHANG D & LIM A. 2015. A variable neighborhood search for the capacitated vehicle routing problem with two-dimensional loading constraints. European Journal of Operational Research , 243(3): 798-814.
|
2L-CVRP |
Sequential and Unrestricted |
≤ |K| |
Yes |
Real |
Variable Neighborhood Search |
Wei et al. (2018)WEI L, ZHANG Z, ZHANG D & LIM A. 2018. A simulated annealing algorithm for the capacitated vehicle routing problem with two-dimensional loading constraints. European Journal of Operational Research , 265: 843-859.
|
2L-CVRP |
Sequential and Unrestricted |
≤ |K| |
Yes |
Real |
Simulated Annealing |
Variants |
Malapert et al. (2008)MALAPERT A, GUERET C, JUSSIEN N, LANGEVIN A & ROUSSEAU LM. 2008. Two-dimensional pickup and delivery routing problem with loading constraints. In: Proceedings of the First CPAIOR Workshop on Bin Packing and Placement Constraints (BPPC’08). pp. 1-46. 4. Paris, France.
|
2L-PDP |
Sequential and Unrestricted |
- |
- |
- |
Constraint Programming |
Munoz (2011)MUNOZ AL. 2011. Solución al problema de ruteo de vehículos con restricciones de capacidad y reordenamiento de carga en los sitios de demanda. Master’s thesis. Escuela de Ingenieria, Pontificia Universidad Catolica de Chile. Santiago, Chile.
|
2L-CVRP-H |
Sequential and Unrestricted |
= |K| |
Yes |
Real |
Mixed-integer Programming |
Khebbache-Hadji et al. (2013)KHEBBACHE-HADJI S, PRINS C, YALAOUI A & REGHIOUI M. 2013. Heuristics and memetic algorithm for the two-dimensional loading capacitated vehicle routing problem with time windows. Central European Journal of Operations Research , 21(2): 307-336.
|
2L-CVRPTW |
Unrestricted |
≤ |K| |
No |
Real |
Memetic Algorithm |
Martínez & Amaya (2013)MARTÍNEZ L & AMAYA CA. 2013. A vehicle routing problem with multi-trips and time windows for circular items. Journal of the Operational Research Society, 64(11): 1630-1643.
|
VRPM-TW-CL |
Unrestricted |
= |K| |
No |
Real |
Tabu Search |
Domínguez et al. (2016)DOMÍNGUEZ O, JUAN AA, BARRIOS B, FAULIN J & AGUSTIN A. 2016. Using biased randomization for solving the two-dimensional loading vehicle routing problem with heterogeneous fleet. Annals of Operations Research , 236(2): 383-404.
|
2L-HFVRP |
Unrestricted |
≤ |K| |
Yes |
Real |
Multistart Biased-Randomized Algorithm |
Zachariadis et al. (2016)ZACHARIADIS EE, TARANTILIS CD & KIRANOUDIS CT. 2016. The Vehicle Routing Problem with Simultaneous Pick-ups and Deliveries and Two-Dimensional Loading Constraints. European Journal of Operational Research , 251(2): 369-386.
|
2L-SPD |
Sequential and Unrestricted |
≤ |K| |
- |
Real |
Local Search |
Côté et al. (2020)CÔTÉ JF, GENDREAU M & POTVIN JY. 2020. The Vehicle Routing Problem with Stochastic Two-Dimensional Items. Transportation Science, 54(2): 453-469.
|
S2L-CVRP |
Sequential |
= |K| |
No |
Integer |
B&C |
Ferreira et al. (2021)FERREIRA KM, QUEIROZ TA & TOLEDO FMB. 2021. An exact approach for the green vehicle routing problem with two-dimensional loading constraints and split delivery. Computers & Operations Research , 136: 105452.
|
2L-SDVRP |
Sequential |
≤ |K| |
Yes |
Integer |
B&C |
G2L-CVRP |
G2L-SDVRP |