Cross dock scheduling under multi-period condition

Document Type : Research Paper


Department of Industrial Engineering, AmirKabir University, Tehran, Iran


This paper proposes a truck scheduling model in a cross dock system under multi-period, multi-commodity condition with fixed outbound departures. In an operational truck scheduling problem, outbound trucks leave the cross dock terminals at predetermined times and delayed loads are kept as inventory that are sent at the next period (a time slot in a day). The proposed model optimizes the inbound truck scheduling problem through the minimizing cross dock operational costs. An accelerated Benders decomposition technique based on Covering Cut Bundle (CCB) strategy and a heuristic approach are developed to solve the model. Finally, numerical analysis introduces the sensitivity of the input parameters to the objective value.


Main Subjects

Alpan, G., Larbi, R., Penz, B., (2011). A bounded dynamic programming approach to schedule operations in a cross docking platform. Comput. Ind. Eng. 60, 385–396.
Bartholdi, J.J., Gue, K.R., (2004). The Best Shape for a Crossdock. Transp. Sci. 38, 235–244.
Benders, J.F., (1962). Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4, 238–252.
Bodnar, P., de Koster, R., Azadeh, K., (2017). Scheduling Trucks in a Cross-Dock with Mixed Service Mode Dock Doors. Transp. Sci. 51, 112–131.
Boysen, N., Briskorn, D., Tschöke, M., (2013). Truck scheduling in cross-docking terminals with fixed outbound departures. OR Spectr. 35, 479–504.
Boysen, N., Fliedner, M., (2010). Cross dock scheduling: Classification, literature review and research agenda. Omega 38, 413–422.
Buijs, P., Vis, I.F.A., Carlo, H.J., (2014). Synchronization in cross-docking networks: A research classification and framework. Eur. J. Oper. Res. 239, 593–608.
Chen, F., Song, K., (2009). Minimizing makespan in two-stage hybrid cross docking scheduling problem. Comput. Oper. Res. 36, 2066–2073.
Cook, R.L., Gibson, B., MacCurdy, D., (2005). A lean approach to cross docking. Supply Chain Manag. Rev. 9, 54–59.
Feo, T.A., Resende, M.G.C., (1989). A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71.
Forouharfard, S., Zandieh, M., (2010). An imperialist competitive algorithm to schedule of receiving and shipping trucks in cross-docking systems. Int. J. Adv. Manuf. Technol. 51, 1179–1193.
Geoffrion, A.., (1972). Generalized Benders Decomposition. J. Optim. Theory Appl. 10, 237–260.
Golshahi-Roudbaneh, A., Hajiaghaei-Keshteli, M., Paydar, M.M., (2019). A hybrid Approach in Metaheuristics for a Cross-dock Scheduling Considering Time Windows and Deadline for Trucks Departure. Sci. Iran. 0–0.
Guemri, O., Nduwayo, P., Todosijević, R., Hanafi, S., Glover, F., (2019). Probabilistic Tabu Search for the Cross-Docking Assignment Problem. Eur. J. Oper. Res. 277, 875–885.
Kaboudani, Y., Ghodsypour, S.H., Kia, H., Shahmardan, A., (2018). Vehicle routing and scheduling in cross docks with forward and reverse logistics. Oper. Res.
Ladier, A.-L., Alpan, G., (2016). Robust cross-dock scheduling with time windows. Comput. Ind. Eng. 99, 16–28.
Ladier, A.., Alpan, G., (2013). Scheduling truck arrivals and departures in a crossdock: Earliness, tardiness and storage policies. Ind. Eng. Syst. Manag. (IESM), Proc. 2013 Int. Conf. 1–7.
Luo, H., Yang, X., Wang, K., (2019). Synchronized scheduling of make to order plant and cross-docking warehouse. Comput. Ind. Eng. 138, 106108.
Mosheiov, G., (1989). Vehicle routing with pick-up and delivery: tour-partitioning heuristics. Comput. Ind. Eng. 34, 669–684.
Nassief, W., Contreras, I., As’ad, R., (2016). A mixed-integer programming formulation and Lagrangean relaxation for the cross-dock door assignment problem. Int. J. Prod. Res. 54, 494–508.
Rahbari, A., Nasiri, M.M., Werner, F., Musavi, M., Jolai, F., (2019). The vehicle routing and scheduling problem with cross-docking for perishable products under uncertainty: Two robust bi-objective models. Appl. Math. Model. 70, 605–625.
Rahmanzadeh Tootkaleh, S., Fatemi Ghomi, S.M.T., Sheikh Sajadieh, M., (2016). Cross dock scheduling with fixed outbound trucks departure times under substitution condition. Comput. Ind. Eng. 92, 50–56.
Rahmanzadeh Tootkaleh, S., Shirazi, M.A., Ghomi, S.M.T.F., Hosseini, S.D., (2014). Truck capacity analysis in a cross‐dock transportation network considering direct shipment. J. Adv. … 48, 891–901.
Saharidis, G.K.D., Minoux, M., Ierapetritou, M.G., (2010). Accelerating Benders method using covering cut bundle generation. Int. Trans. Oper. Res. 17, 221–237.
Shahmardan, A., Sajadieh, M.S., (2020). Truck scheduling in a multi-door cross-docking center with partial unloading – Reinforcement learning-based simulated annealing approaches. Comput. Ind. Eng. 139, 106134.
Shiguemoto, A.., Netto, U.S.., Bauab, G.H.S., (2014). An efficient hybrid meta-heuristic for a cross-docking system with temporary storage. Int. J. Prod. Res. 52, 1231–1239.
Soltani, R., Sadjadi, S.J., (2010). Scheduling trucks in cross-docking systems: A robust meta-heuristics approach. Transp. Res. Part E Logist. Transp. Rev. 46, 650–666.
Stalk, G., Evans, P., Shulman, L., (1992). Competing on capabilities: The New Rules of Corporate Strategy. Harv. Bus. Rev. 70, 57–69.
Theophilus, O., Dulebenets, M.A., Pasha, J., Abioye, O.F., Kavoosi, M., (2019). Truck Scheduling at Cross-Docking Terminals: A Follow-Up State-Of-The-Art Review. Sustainability 11, 5245.
Van Belle, J., Valckenaers, P., Cattrysse, D., (2012). Cross-docking: State of the art. Omega 40, 827–846.
Wang, H., Alidaee, B., (2019). The multi-floor cross-dock door assignment problem: Rising challenges for the new trend in logistics industry. Transp. Res. Part E Logist. Transp. Rev. 132, 30–47.
Witt, C.E., (1998). Cross docking: Concepts demand choice. Mater. Handl. Eng. 53, 44–49.
Yu, V., Jewpanya, P., Kachitvichyanukulb, V., (2015). Particle swarm optimization for the multi-period cross-docking distribution problem with time windows. Int. J. Prod. Res. 54, 509–525.
Zarandi, M.H.F., Khorshidian, H., Shirazi, M.A., (2014). A constraint programming model for the scheduling of JIT cross-docking systems with preemption. J. Intell. Manuf. 27, 297–313.
Volume 12, Issue 4 - Serial Number 4
November 2019
Pages 208-226
  • Receive Date: 04 June 2019
  • Revise Date: 19 February 2020
  • Accept Date: 19 February 2020
  • First Publish Date: 19 February 2020