A Novel Mathematical Model for Cross Dock Open-Close Vehicle Routing Problem with Splitting

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Mahdi Alinaghian 1,* Mina Rezaei Kalantari 1 Ali Bozorgi-Amiri 2 Nima Golghamat Raad 1

1. Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan, Iran

2. School of Industrial Engineering, College of Engineering, University of Tehran,Iran

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2016.03.02

Received: 3 Apr. 2016 / Revised: 7 May 2016 / Accepted: 1 Jun. 2016 / Published: 8 Jul. 2016

Index Terms

Cross dock, open-close vehicle routing problem (OCVRP), vehicle routing problem with splitting delivery (VRPSD), simulated annealing algorithm (SAA)


Cross docks play an important role in goods distribution. In most of the common models, the capacity of vehicles is not completely used as they assume that each node is met only by one vehicle. Also, due to high cost of purchasing vehicles with high capacity, rental vehicles are used in collecting section. In this paper, a novel mathematical model is presented in which, each node can be possibly visited by different vehicles (splitting). Besides, in the proposed model, existence of open routes in pickup section has been supposed. Then, one meta-heuristic method based on the simulation annealing algorithm with two different approaches has been developed. For testing the performance of the proposed algorithm, the obtained results compared with the exact answers in both small and large scales. The outcomes show that the algorithm works properly.

Cite This Paper

Mahdi Alinaghian, Mina Rezaei Kalantari, Ali Bozorgi-Amiri, Nima Golghamat Raad,"A Novel Mathematical Model for Cross Dock Open-Close Vehicle Routing Problem with Splitting", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.2, No.3, pp.21-31, 2016.DOI: 10.5815/ijmsc.2016.03.02


[1]Van Belle, J., Valckenaers, P., & Cattrysse, D. (2012). Cross-docking: State of the art. Omega, 40(6), 827-846.

[2]Santos, F. A., Mateus, G. R., & Da Cunha, A. S. (2013). The pickup and delivery problem with cross-docking. Computers & Operations Research, 40(4), 1085-1093. 

[3]Moghadam, S. S., Ghomi, S. F., & Karimi, B. (2014). Vehicle routing scheduling problem with cross docking and split deliveries. Computers & Chemical Engineering, 69, 98-107. 

[4]Mousavi, S. M., & Tavakkoli-Moghaddam, R. (2013). A hybrid simulated annealing algorithm for location and routing scheduling problems with cross-docking in the supply chain. Journal of Manufacturing Systems, 32(2), 335-347. 

[5]Hasani-Goodarzi, A., & Tavakkoli-Moghaddam, R. (2012). Capacitated vehicle routing problem for multi-product cross-docking with split deliveries and pickups. Procedia-Social and Behavioral Sciences, 62, 1360-1365.

[6]Sung, C. S., & Song, S. H. (2003). Integrated service network design for a cross-docking supply chain network. Journal of the Operational Research Society, 54(12), 1283-1295.

[7]Hu, Z. H., Zhao, Y., & Choi, T. M. (2013). Vehicle routing problem for fashion supply chains with cross-docking. Mathematical problems in Engineering, 2013. 

[8]Mousavi, S. M., Vahdani, B., Tavakkoli-Moghaddam, R., & Hashemi, H. (2014). Location of cross-docking centers and vehicle routing scheduling under uncertainty: a fuzzy possibilistic–stochastic programming model. Applied Mathematical Modelling, 38(7), 2249-2264.

[9]Dondo, R., & Cerdá, J. (2015). The heterogeneous vehicle routing and truck scheduling problem in a multi-door cross-dock system. Computers & Chemical Engineering, 76, 42-62.

[10]Oh, Y., Hwang, H., Cha, C. N., & Lee, S. (2006). A dock-door assignment problem for the Korean mail distribution center. Computers & Industrial Engineering, 51(2), 288-296.

[11]Miao, Z., Lim, A., & Ma, H. (2009). Truck dock assignment problem with operational time constraint within crossdocks. European journal of operational research, 192(1), 105-115.

[12]Miao, Z., Cai, S., & Xu, D. (2014). Applying an adaptive tabu search algorithm to optimize truck-dock assignment in the crossdock management system. Expert Systems with Applications, 41(1), 16-22.

[13]Kuo, Y. (2013). Optimizing truck sequencing and truck dock assignment in a cross docking system. Expert Systems with Applications, 40(14), 5532-5541. 

[14]Konur, D., & Golias, M. M. (2013). Cost-stable truck scheduling at a cross-dock facility with unknown truck arrivals: A meta-heuristic approach. Transportation Research Part E: Logistics and Transportation Review, 49(1), 71-91.

[15]Madani-Isfahani, M., Tavakkoli-Moghaddam, R., & Naderi, B. (2014). Multiple cross-docks scheduling using two meta-heuristic algorithms. Computers & Industrial Engineering, 74, 129-138. 

[16]Lee, Y. H., Jung, J. W., & Lee, K. M. (2006). Vehicle routing scheduling for cross-docking in the supply chain. Computers & Industrial Engineering, 51(2), 247-256.

[17]Liao, C. J., Lin, Y., & Shih, S. C. (2010). Vehicle routing with cross-docking in the supply chain. Expert Systems with Applications, 37(10), 6868-6873.

[18]Morais, V. W., Mateus, G. R., & Noronha, T. F. (2014). Iterated local search heuristics for the vehicle routing problem with cross-docking. Expert Systems with Applications, 41(16), 7495-7506.

[19]Agustina, D., Lee, C. K. M., & Piplani, R. (2014). Vehicle scheduling and routing at a cross docking center for food supply chains. International Journal of Production Economics, 152, 29-41.

[20]Vincent, F. Y., Jewpanya, P., & Redi, A. P. (2016). Open Vehicle Routing Problem with Cross-Docking. Computers & Industrial Engineering.

[21]Moshizi, M. M., & Bardsiri, A. K. (2015). The Application of Meta-Heuristic Algorithms in Automatic Software Test Case Generation. IJMSC-International Journal of Mathematical Sciences and Computing (IJMSC), 1(3), 1.

[22]Kirkpatrick, S. (1984). Optimization by simulated annealing: Quantitative studies. Journal of statistical physics, 34(5-6), 975-986.