A Multi-Objective Optimization Model for Split Pollution Routing Problem with Controlled Indoor Activities in Cross Docking under Uncertainty

Document Type : Research Paper


1 Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 1Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran


Cross docking is a logistics strategy that strives to reduce inventory holding costs, shipping costs, and delays in delivering the products. In this research, an optimization model is presented for split loading and unloading products by suppliers and customers, vehicle routing with fuzzy possibilistic time window constraints among them, assignment of vehicles to cross dock, consolidation and integration of products in cross dock, and allocation of sorted products to outbound vehicles. The mathematical model provided in this study has three objective functions. The first and second objectives minimize total cost and fuel consumption, and the third one maximizes satisfaction degrees of suppliers and customers. With the intention of solving the model, two multi-objective meta-heuristic algorithms, namely Multi-Objective Grey Wolf Optimizer (MOGWO) and Multi-Objective Imperialist Competitive Algorithm (MOICA) were utilized. With the intention of illustrating the accuracy of the suggested model and solution approaches, a broad range of numerical instances were considered and the results were investigated.


Abad, H. K., Vahdani, B., Sharifi, M., & Etebari, F. (2018). A bi-objective model for pickup and delivery pollution-routing problem with integration and consolidation shipments in cross-docking system. Journal of Cleaner Production, 193(20), 784-801.
Adewale, P., Vithanage, L. N., & Christopher, L. (2017). Optimization of enzyme-catalyzed biodiesel production from crude tall oil using Taguchi method. Energy Conversion and Management, 154, 81-91.
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.
Ahkamiraad, A., & Wang, Y. (2018). Capacitated and multiple cross-docked vehicle routing problem with pickup, delivery, and time windows. Computers & Industrial Engineering, 119, 76-84.
Amini, M. H., Boroojeni, K. G., Iyengar, S. S., Blaabjerg, F., Pardalos, P. M., & Madni, A. M. (2018). A Panorama of Future Interdependent Networks: From Intelligent Infrastructures to Smart Cities. In Sustainable Interdependent Networks (pp. 1-10). Cham: Springer.
Apte, U. M., & Viswanathan, S. (2000). Effective cross docking for improving distribution efficiencies. International Journal of Logistics, 3(3), 291-302.
Baniamerian, A., Bashiri, M., & Tavakkoli-Moghaddam, R. (2019). Modified variable neighborhood search and genetic algorithm for profitable heterogeneous vehicle routing problem with cross-docking. Applied Soft Computing, 75, 441-460.
Barth, M., & Boriboonsomsin, K. (2008). Real-world carbon dioxide impacts of traffic congestion. Transportation Research Record: Journal of the Transportation Research Board, 2058, 163-171.
Barth, M., Younglove, T., & Scora, G. (2005). Development of a heavy-duty diesel modal emissions and fuel consumption model. California Partners for Advanced Transportation Technology (PATH).
Bhangu, M. S., Anand, R., & Kumar, V. (2019). Lagrangian relaxation for distribution networks with cross-docking centre. International Journal of Intelligent Systems Technologies and Applications, 18(1-2), pp.52-68.
Bodnar, P., de Koster, R., & Azadeh, K. (2015). Scheduling Trucks in a Cross-Dock with Mixed Service Mode Dock Doors. Transportation Science, 51(1), 112-131.
Chaleshtari, M. H. B., & Jafari, M. (2017). Optimized design for perforated plates with quasi-square hole by grey wolf optimizer. Structural Engineering and Mechanics, 63(3), 269-280.
Coello Coello, C. A. (2000). MOPSO: A proposal for multiple objective particle swarm optimization. In Proceedings of the 2002 Congress on Evolutionary Computation (CEC 2002), (Vol. 2, pp. 1051-1056).
Deb, K., Agrawal, S., Pratap, A., & Meyarivan, T. (2000). A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In International Conference on Parallel Problem Solving From Nature (pp. 849-858). Berlin, Heidelberg: Springer.
Dondo, R., Méndez, C. A., & Cerdá, J. (2011). The multi-echelon vehicle routing problem with cross docking in supply chain management. Computers & Chemical Engineering, 35(12), 3002-3024.
Enderer, F., Contardo, C., & Contreras, I. (2017). Integrating dock-door assignment and vehicle routing with cross-docking. Computers & Operations Research, 88, 30-43.
Heidari, F., Zegordi, S. H., & Tavakkoli-Moghaddam, R. (2018). Modeling truck scheduling problem at a cross-dock facility through a bi-objective bi-level optimization approach. Journal of Intelligent Manufacturing, 29(5), 1155-1170.
Hosseini, S., & Al Khaled, A. (2014). A survey on the imperialist competitive algorithm metaheuristic: implementation in engineering domain and directions for future research. Applied Soft Computing, 24, 1078-1094.
Huang, Y., Shi, C., Zhao, L., & Van Woensel, T. (2012). A study on carbon reduction in the vehicle routing problem with simultaneous pickups and deliveries. In Service Operations and Logistics, and Informatics (SOLI), 2012 IEEE International Conference (pp. 302-307). IEEE.
Jadaan, O. A., Rajamani, L., & Rao, C. R. (2009). Non-Dominated Ranked Genetic Algorithm for Solving Constrained Multi-Objective Optimization Problems. Journal of Theoretical & Applied Information Technology, 5(5).
Javanmard, S., Vahdani, B., & Tavakkoli-Moghaddam, R. (2014). Solving a multi-product distribution planning problem in cross docking networks: An imperialist competitive algorithm. The International Journal of Advanced Manufacturing Technology, 70(9-12), 1709-1720.
Kennedy, J., Eberhart, R. C., & Shi, Y. (2001). Swarm intelligence. (Vol. 1, pp. 700-720). San Francisco: Kaufmann.
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.
Kuo, Y. (2013). Optimizing truck sequencing and truck dock assignment in a cross docking system. Expert Systems with Applications, 40(14), 5532-5541.
Ladier, A. L., & Alpan, G. (2016). Cross-docking operations: Current research versus industry practice. Omega, 62, 145-162.
Liao, C. J., Lin, Y., & Shih, S. C. (2010). Vehicle routing with cross-docking in the supply chain. Expert Systems with Applications, 37, 6868–6873.
Liao, T. W., Egbelu, P. J., & Chang, P. C. (2013). Simultaneous dock assignment and sequencing of inbound trucks under a fixed outbound truck schedule in multi-door cross docking operations. International Journal of Production Economics, 141(1), 212-229.
Lu, Z., & Bostel, N. (2007). A facility location model for logistics systems including reverse flows: The case of remanufacturing activities. Computers & Operations Research, 34(2), 299-323.
Mohammadi, M., Dehbari, S., & Vahdani, B. (2014). Design of a bi-objective reliable healthcare network with finite capacity queue under service covering uncertainty. Transportation Research Part E: Logistics and Transportation Review, 72, 15-41.
Mousavi, S. M., Alikar, N., Niaki, S. T. A., & Bahreininejad, A. (2015). Two tuned multi-objective meta-heuristic algorithms for solving a fuzzy multi-state redundancy allocation problem under discount strategies. Applied Mathematical Modelling, 39(22), 6968-6989.
Mousavi, S. M., Antuchevičienė, J., Zavadskas, E. K., Vahdani, B., & Hashemi, H. (2019). A new decision model for cross-docking center location in logistics networks under interval-valued intuitionistic fuzzy uncertainty. Transport, 34(1), 30-40.
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(7-8), 2249-2264.
Mousavi, S. M., & Vahdani, B. (2016). Cross-docking location selection in distribution systems: a new intuitionistic fuzzy hierarchical decision model. International Journal of Computational Intelligence Systems, 9(1), 91-109.
Mousavi, S. M., & Vahdani, B. (2017). A robust approach to multiple vehicle location-routing problems with time windows for optimization of cross-docking under uncertainty. Journal of Intelligent & Fuzzy Systems, 32(1), 49-62.
Musa, R., Arnaout, J. P., & Jung, H. (2010). Ant colony optimization algorithm to solve for the transportation problem of cross-docking network. Computers & Industrial Engineering, 59(1), 85-92.
Niakan, F., Vahdani, B., & Mohammadi, M. (2015). A multi-objective optimization model for hub network design under uncertainty: An inexact rough-interval fuzzy approach. Engineering Optimization, 47(12), 1670-1688.
Niu, Y., Yang, Z., Chen, P., & Xiao, J. (2018). Optimizing the green open vehicle routing problem with time windows by minimizing comprehensive routing cost. Journal of Cleaner Production, 171, 962-971.
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.
Park, Y., & Chae, J. (2014). A review of the solution approaches used in recent G-VRP (Green Vehicle Routing Problem). International Journal of Advanced Logistics, 3(1-2), 27-37.
Serrano, C., Delorme, X., & Dolgui, A. (2017). Scheduling of truck arrivals, truck departures and shop-floor operation in a cross-dock platform, based on trucks loading plans. International Journal of Production Economics, 194, 102-112.
Scora, G., & Barth, M. (2006). Comprehensive modal emissions model (cmem), version 3.01. User guide. Centre for Environmental Research and Technology. Riverside: University of California.
Shaelaie, M. H., Ranjbar, M., & Jamili, N. (2018). Integration of parts transportation without cross docking in a supply chain. Computers & Industrial Engineering, 118, 67-79.
Shakeri, M., Low, M. Y. H., Turner, S. J., & Lee, E. W. (2012). A robust two-phase heuristic algorithm for the truck scheduling problem in a resource-constrained crossdock. Computers & Operations Research, 39(11), 2564-2577.
Tajik, N., Tavakkoli-Moghaddam, R., Vahdani, B., & Mousavi, S. M. (2014). A robust optimization approach for pollution routing problem with pickup and delivery under uncertainty. Journal of Manufacturing Systems, 33(2), 277-286.
Tanaka, S., Detienne, B., & Sadykov, R. (2018). Time-indexed Formulations of the Truck-to-door Scheduling Problem at Multi-door Cross-docking Terminals with Temporary Storage. Proceedings of the International Symposium on Flexible Automation, 377-382.
Tavana, M., Khalili-Damghani, K., Santos-Arteaga, F. J., & Zandi, M. H. (2017). Drone shipping versus truck delivery in a cross-docking system with multiple fleets and products. Expert Systems with Applications, 72, 93-107.
Tootkaleh, S. R., Ghomi, S. F., & Sajadieh, M. S. (2016). Cross dock scheduling with fixed outbound trucks departure times under substitution condition. Computers & Industrial Engineering, 92, 50-56.
Toro, E. M., Franco, J. F., Echeverri, M. G., & Guimarães, F. G. (2017). A multi-objective model for the green capacitated location-routing problem considering environmental impact. Computers & Industrial Engineering, 110, 114-125.
Vahdani, B., Niaki, S. T. A., Aslanzade, S. (2017). Production-inventory-routing coordination with capacity and time window constraints for perishable products: Heuristic and meta-heuristic algorithms. Journal of Cleaner Production, 161, 598-618.
Vahdani, B., Razmi, J., & Tavakkoli-Moghaddam, R. (2012a). Fuzzy possibilistic modeling for closed loop recycling collection networks. Environmental Modeling & Assessment, 17(6), 623-637.
Vahdani, B., Soltani, R., & Zandieh, M. (2010). Scheduling the truck holdover recurrent dock cross-dock problem using robust meta-heuristics. The International Journal of Advanced Manufacturing Technology, 46(5-8), 769-783.
Vahdani, B., Tavakkoli-Moghaddam, R., Zandieh, M., & Razmi, J. (2012b). Vehicle routing scheduling using an enhanced hybrid optimization approach. Journal of Intelligent Manufacturing, 23(3), 759-774.
Vahdani, B., Veysmoradi, D., Noori, F., & Mansour, F. (2018). Two-stage multi-objective location-routing-inventory model for humanitarian logistics network design under uncertainty. International Journal of Disaster Risk Reduction, 27, 290-306.
Vahdani, B., Veysmoradi, D., Shekari, N., & Mousavi, S. M. (2016). Multi-objective, multi-period location-routing model to distribute relief after earthquake by considering emergency roadway repair. Neural Computing and Applications, 1-20.
Vahdani, B. & Zandieh, M. (2010). Scheduling trucks in cross-docking systems: Robust meta-heuristics. Computers & Industrial Engineering, 58(1), 12-24.
Van Belle, J., Valckenaers, P., & Cattrysse, D. (2012). Cross-docking: State of the art. Omega, 40(6), 827-846.
Vincent, F. Y., Jewpanya, P., & Redi, A. P. (2016). Open vehicle routing problem with cross-docking. Computers & Industrial Engineering, 94, 6-17.
Wang, J., Jagannathan, A. K. R., Zuo, X., & Murray, C. C. (2017). Two-layer simulated annealing and tabu search heuristics for a vehicle routing problem with cross docks and split deliveries. Computers & Industrial Engineering, 112, 84-98.
Wen, M., Larsen, J., Clausen, J., Cordeau, J. F., & Laporte, G. (2009). Vehicle routing with cross-docking. Journal of the Operational Research Society, 60, 1708 -1718.
Wisittipanich, W., & Hengmeechai, P. (2017). Truck scheduling in multi-door cross docking terminal by modified particle swarm optimization. Computers & Industrial Engineering, 113, 793-802.
Yan, H., & Tang, S. L. (2009). Pre-distribution and post-distribution cross-docking operations. Transportation Research Part E: Logistics and Transportation Review, 45(6), 843-859.
Ye, Y., Li, J. F., Fung, R. Y., Li, K., & Fu, H. (2018b). Optimizing truck scheduling in a cross-docking system with preemption and unloading/loading sequence constraint. In 2018 IEEE 15th International Conference on Networking, Sensing and Control (ICNSC) (pp. 1-6). IEEE.
Ye, Y., Li, J., Li, K., & Fu, H. (2018a). Cross-docking truck scheduling with product unloading/loading constraints based on an improved particle swarm optimisation algorithm. International Journal of Production Research, 56(16), 5365-5385.
Yin, P. Y., & Chuang, Y. L. (2016). Adaptive memory artificial bee colony algorithm for green vehicle routing with cross-docking. Applied Mathematical Modelling, 40(21), 9302-9315.
Yu, W., & Egbelu, P. J. (2008). Scheduling of inbound and outbound trucks in cross docking systems with temporary storage. European Journal of Operational Research, 184(1), 377-396.
Zandieh, M., Amiri, M., Vahdani, B., & Soltani, R. (2009). A robust parameter design for multi-response problems. Journal of computational and applied mathematics, 230(2), 463-476.
Zhou, G., & Zhang, Y. (2017). Integration and consolidation in air freight shipment planning: An economic and environmental perspective. Journal of Cleaner Production, 166, 1381-1394.