Automatic Reverse Warehousing System: Principal Concepts, Modeling and Optimizing of Shelving and Routing Problems

Document Type : Research Paper


Faculty of Industrial Engineering, Tarbiat Modares University, Tehran, Iran


Warehouses and distribution centers are essential components in supply chain and their management has a particular importance. In the traditional approach for collecting the items of orders in warehouses, operators walk or drive toward the shelves and collect the ordered items. However, since 2006 a new system has been deployed in some large distributing warehouses like Amazon Inc., in which shelves are mounted on mobile platforms and are carried by small mobile robots toward operators who pick the ordered items. Advantages of this system compared to traditional system are increased flexibility, accuracy, and speed of preparing the received orders. On the other hand, the mathematical model of this system –which we call it ‘Automatic Reverse Warehousing System (ARWS)’– is introduces as a trade solution, and no research papers have been published about it. In this paper, this system will be studied from the viewpoint of industrial engineering. Then, its components and their relationship with each other and their two major subproblems, namely, allocation and routing will be identified, and their interrelations will be investigated. The model is solved for minimizing the overall cost and finding the best paths of shelves through a Genetic Algorithm and maximum flow approach.


  1. Wurman, P.R., D’Andrea, R. and Mountz, M. (2008). “Coordinating hundreds of cooperative, autonomous vehicles in warehouses”, AI Magazine, Vol. 29, No. 1, PP. 9–20.
  2. Lesser, V.R. (1999). “Cooperative multiagent systems: A personal view of the state of the art”, IEEE Transactions on Knowledge and Data Engineering,Vol. 11, No. 1, PP. 133–142.
  3. De Koster, R., Le-Duc, T. and Roodbergen, K.J. (2007). “Design and control of warehouse order picking: A literature review”, European Journal of Operational Research, Vol. 182, No. 2, PP. 481–501.
  4. Wurman, P.R., D’Andrea, R. and Mountz, M. (2008). “Coordinating hundreds of cooperative, autonomous vehicles in warehouses”, AI Magazine, Vol. 29, No. 1, PP. 9–20.
  5. Guerriero, F., Musmanno, R., Pisacane, O. and Rende, F. (2013). “A mathematical model for the multi-levels product allocation problem in a warehouse with compatibility constraints”, Applied Mathematical Modeling, Vol. 37, No. 6, PP. 4385–4398.
  6. Muppani, V.R. and Adil G.K. (2006). “Formation of storage classes in the presence of space cost for warehouse planning”, International Journal of Services Operations and Informatics, Vol. 1, No. 3, PP. 286–303.
  7. Heragu, S.S. (2005). “Mathematical model for warehouse design and product allocation”, Int. J. Production Research, Vol. 43, No. 2, PP. 327–338.
  8. Önüt, S., Tuzkaya, U.R. and Doga B. (2008). “A particle swarm optimization algorithm for the multiple-level warehouse layout design problem”, Computers and Industrial Engineering, Vol. 54, No. 4, PP. 783–799.
  9. Sanei, O., Nasiri, V., Marjani, M.R. and Moattar-Husseini, S.M. (2011). “A heuristic algorithm for the warehouse space assignment problem considering operational constraints: with application in a case study”, Proc. 2011 Int. Conf. on Industrial Engineering and Operations Management, Kuala Lumpur, Malaysia, January 22–24.

10. Bektas, T. (2006). “The multiple traveling salesman problem: an overview of formulations and solution procedures”, Omega, Vol. 34, No. 3, PP. 209–219.

11. Theys, C., Broysy, O., Dullaert, W., Raa. (2010). “Using a TSP heuristic for routing order pickers in warehouses”, European Journal of Operational Research, PP. 755–763.

12. Norouzi, N., et al. (2015). “New mathematical modeling for a facilities location and vehicle routing problem solving by a hybrid imperialist competitive algorithm”,  Journal of Industrial Engineering, vol 49, No 1 , PP. 129–137.

13. Parragh, S., Doerner, K. and Hart, R. (2008). “A survey on pickup and delivery problems: Part I, Transportation between customers and depot”, Journal für Betriebswirtschaft, Vol. 58, No. 1, PP. 21–51.

14. Pandelis, D.G., Karamatsoukis, C. and Kyriakidis, G. (2013). “Single vehicle routing problems with a predefined customer order, unified load and stochastic discrete demands”, Probability in the Engineering and Informational Sciences, Vol. 27. No. 1, PP. 1–23.

15. Setak, M., Jalili Bolhassani, S., Karimi, H. and Gorbani, B. (2014). “A node-based mathematical model towards the location routing problem with intermediate replenishment facilities under capacity constraint”, International Journal of Engineering, Vol. 27, No. 6, PP. 911–20.

16. Davoodi, M., Abedin, M., Banyassady, B., Khanteimouri, P. and Mohades A. (2013). “An optimal algorithm for two robots path planning problem on the grid”, Robotics and Autonomous Systems, Vol. 61, No. 12, PP. 1406–1414.

17. Roozbehani, H. and D’Andrea R. (2011). “Adaptive highways on a grid”, In Pradalier, C., Siegwart, R., and Hirzinger, G. (Eds.), Robotics Research, Vol. 70. Springer Berlin/Heidelberg, PP. 661–680.

18. Yu, J. and LaValle, S.M. (2013). “Planning optimal paths for multiple robots on graphs”, Proc. IEEE Int. Conf. on Robotics and Automation (ICRA), May 2013, Kalsruhe, Germany, PP. 3612-3617.

19. Surynek, P. (2010). “An optimization variant of multi-robot path planning is intractable”, Proc. of the 24thAAAI Conference on Artificial Intelligence, PP. 1261–1263.

20. Bruno, J., Coffmann, E. and Sethi, R. (1974). “Scheduling independent tasks to reduce mean finishing time”, Communications of ACM, Vol. 17, No. 7, PP. 382–387.

  1. Parekh, A. (2016). “Kiva Systems–Robotic Warehouse”, Available online at 2010/07/10/kiva-systems-robotic-warehouse.