New Approaches in Metaheuristics to Solve the Truck Scheduling Problem in a Cross-docking Center


1 Department of Mathematics and Computer Science, University of Science and Technology of Mazandaran, Behshahr, Iran

2 Department of Industrial Engineering, University of Science and Technology of Mazandaran, Behshahr, Iran


Nowadays, cross-docking is one of the main concepts in supply chain management in which products received to a distribution center by inbound trucks which are directly to lead into outbound trucks with a minimum handling and storage costs as the main cost of a cross-docking system. According to the literature, several metaheuristics and heuristics are attempted to solve this optimization model. In this regard, this study utilizes three recent nature-inspired metaheuristics among the first studies in this area. Red Deer Algorithm (RDA), Virus Colony Search (VCS) and Water Wave Optimization (WWO) are three novel nature-inspired algorithms proposed recently to employ their applications in engineering problems. The used algorithm’s parameters were selected by Taguchi method to enhance the efficiency of algorithms. The outputs of the proposed algorithms are assessed with each other in different criteria along with statistical analyses and the results yielded by prior works. The results demonstrate that RDA showed a competitive performance compared with mixed other existing algorithms.


1.     Sadeghi-Moghaddam, S., Hajiaghaei-Keshteli, M. and Mahmoodjanloo, M., "New approaches in metaheuristics to solve the fixed charge transportation problem in a fuzzy environment", Neural Computing and Applications,  (2017), 1-21.
2.     Nourmohamadi Shalke, P., Paydar, M.M. and Hajiaghaei-Keshteli, M., "Sustainable supplier selection and order allocation through quantity discounts", International Journal of Management Science and Engineering Management,  Vol. 13, No. 1, (2018), 20-32.
3.     Fard, A.M.F., Gholian-Jouybari, F., Paydar, M.M. and Hajiaghaei-Keshteli, M., "A bi-objective stochastic closed-loop supply chain network design problem considering downside risk", Industrial Engineering & Management Systems,  Vol. 16, No. 3, (2017), 342-362.
4.     Fard, A.M.F. and Hajiaghaei-Keshteli, M., "A bi-objective partial interdiction problem considering different defensive systems with capacity expansion of facilities under imminent attacks", Applied Soft Computing,  Vol. 68, (2018), 343-359.
5.     Chen, F. and Song, K., "Minimizing makespan in two-stage hybrid cross docking scheduling problem", Computers & Operations Research,  Vol. 36, No. 6, (2009), 2066-2073.
6.     Wisittipanich, W. and Hengmeechai, P., "Truck scheduling in multi-door cross docking terminal by modified particle swarm optimization", Computers & Industrial Engineering,  Vol. 113, (2017), 793-802.
7.     Golshahi-Roudbaneh, A., Hajiaghaei-Keshteli, M. and Paydar, M.M., "Developing a lower bound and strong heuristics for a truck scheduling problem in a cross-docking center", Knowledge-Based Systems,  Vol. 129, (2017), 17-38.
8.     Yu, W. and Egbelu, P.J., "Scheduling of inbound and outbound trucks in cross docking systems with temporary storage", European Journal of Operational Research,  Vol. 184, No. 1, (2008), 377-396.
9.     Bellanger, A., Hanafi, S. and Wilbaut, C., "Three-stage hybrid-flowshop model for cross-docking", Computers & Operations Research,  Vol. 40, No. 4, (2013), 1109-1121.
10.   Larbi, R., Alpan, G., Baptiste, P. and Penz, B., "Scheduling cross docking operations under full, partial and no information on inbound arrivals", Computers & Operations Research,  Vol. 38, No. 6, (2011), 889-900.
11.   Amini, A. and Tavakkoli-Moghaddam, R., "A bi-objective truck scheduling problem in a cross-docking center with probability of breakdown for trucks", Computers & Industrial Engineering,  Vol. 96, (2016), 180-191.
12.   Dondo, R. and Cerdá, J., "A sweep-heuristic based formulation for the vehicle routing problem with cross-docking", Computers & Chemical Engineering,  Vol. 48, (2013), 293-311.
13.   Dondo, R. and Cerdá, J., "The heterogeneous vehicle routing and truck scheduling problem in a multi-door cross-dock system", Computers & Chemical Engineering,  Vol. 76, (2015), 42-62.
14.   Morais, V.W., Mateus, G.R. and Noronha, T.F., "Iterated local search heuristics for the vehicle routing problem with cross-docking", Expert Systems with Applications,  Vol. 41, No. 16, (2014), 7495-7506.
15.   Yin, P.-Y., Lyu, S.-R. and Chuang, Y.-L., "Cooperative coevolutionary approach for integrated vehicle routing and scheduling using cross-dock buffering", Engineering Applications of Artificial Intelligence,  Vol. 52, (2016), 40-53.
16.   Grangier, P., Gendreau, M., Lehuédé, F. and Rousseau, L.-M., "A matheuristic based on large neighborhood search for the vehicle routing problem with cross-docking", Computers & Operations Research,  Vol. 84,  (2017), 116-126.
17.   Stephan, K., Boysen, N. and Cross-docking, J., "Manage", Control,  Vol. 22, (2011), 129-137.
18.   Van Belle, J., Valckenaers, P. and Cattrysse, D., "Cross-docking: State of the art", Omega,  Vol. 40, No. 6, (2012), 827-846.
19.   Zuluaga, J.P.S., Thiell, M. and Perales, R.C., "Reverse cross-docking", Omega,  Vol. 66, (2017), 48-57.
20.   Boysen, N. and Fliedner, M., "Cross dock scheduling: Classification, literature review and research agenda", Omega,  Vol. 38, No. 6, (2010), 413-422.
21.   Ladier, A.-L. and Alpan, G., "Cross-docking operations: Current research versus industry practice", Omega,  Vol. 62, (2016), 145-162.
22.   Madani-Isfahani, M., Tavakkoli-Moghaddam, R. and Naderi, B., "Multiple cross-docks scheduling using two meta-heuristic algorithms", Computers & Industrial Engineering,  Vol. 74, (2014), 129-138.
23.   Cota, P.M., Gimenez, B.M., Araújo, D.P., Nogueira, T.H., de Souza, M.C. and Ravetti, M.G., "Time-indexed formulation and polynomial time heuristic for a multi-dock truck scheduling problem in a cross-docking centre", Computers & Industrial Engineering,  Vol. 95,  (2016), 135-143.
24.   Hajiaghaei-Keshteli, M. and Sajadifar, S.M., "Deriving the cost function for a class of three-echelon inventory system with n-retailers and one-for-one ordering policy", The International Journal of Advanced Manufacturing Technology,  Vol. 50, No. 1-4, (2010), 343-351.
25.   Hajiaghaei-Keshteli, M. and Fard, A.M.F., "Sustainable closed-loop supply chain network design with discount supposition", Neural Computing and Applications,   (2018), 1-35.
26.   Samadi, A., Mehranfar, N., Fathollahi Fard, A. and Hajiaghaei-Keshteli, M., "Heuristic-based metaheuristics to address a sustainable supply chain network design problem", Journal of Industrial and Production Engineering,  Vol. 35, No. 2, (2018), 102-117.
27.   Fard, A.F. and Hajiaghaei-Keshteli, M., "Red deer algorithm (rda); a new optimization algorithm inspired by red deers’ mating", in International Conference on Industrial Engineering, IEEE., (2016), 33-34.
28.   Golmohamadi, S., Tavakkoli-Moghaddam, R. and Hajiaghaei-Keshteli, M., "Solving a fuzzy fixed charge solid transportation problem using batch transferring by new approaches in meta-heuristic", Electronic Notes in Discrete Mathematics,  Vol. 58, (2017), 143-150.
29.   Li, M.D., Zhao, H., Weng, X.W. and Han, T., "A novel nature-inspired algorithm for optimization: Virus colony search", Advances in Engineering Software,  Vol. 92, (2016), 65-88.
30.   Zheng, Y.-J., "Water wave optimization: A new nature-inspired metaheuristic", Computers & Operations Research,  Vol. 55, (2015), 1-11.
31.   Fathollahi-Fard, A.M. and Hajiaghaei-Keshteli, M., "A stochastic multi-objective model for a closed-loop supply chain with environmental considerations", Applied Soft Computing,  Vol. 69, (2018), 232-249.
32.   Fard, A.M.F. and Hajaghaei-Keshteli, M., "A tri-level location-allocation model for forward/reverse supply chain", Applied Soft Computing,  Vol. 62, (2018), 328-346.
33.   Nasiri, E., Afshari, A. and Hajiaghaei-Keshteli, M., "Addressing the freight consolidation and containerization problem by recent and hybridized meta-heuristic algorithms", International Journal of Engineering-Transactions C: Aspects,  Vol. 30, No. 3, (2017), 403-410.
34.   Taguchi, G. and Clausing, D., "Robust quality", Harvard Business Review,  Vol. 68, No. 1, (1990), 65-75.