Optimal Routing in an Automated Warehouse with 2-nested GTSP

In recent years storage systems have extremely developed. These developments are in both hardware perspective like as storage cells design and automated storage and retrieval machines and software perspective like as travel-time model and equipment usage strategy. Automated storage and retrieval systems development is one of these efforts in industrial modernization.In this paper the process of storage and retrieve material in automated storage and retrieval system has been modeled according to orders including some items into a new model that has been introduced in this paper. The term 2-nested generalized traveling salesman problem (2-nested GTSP) has been coined for the model. The authors showed that the problem of picking an order’s items could be modeled with 2-nested GTSP easily. Then a mathematical model of the problem was developed and solved with LINGO. Since the problem is NP-Hard, it was solved with a meta-heuristic algorithm ACSrank. The algorithm ACSrank is a new version of ACO that was developed and have ASrank and ACS features. The results of mathematical model and ACSrank algorithm are compared. Both of them have the same answer in 8 test problems. In problems 9, 10 and 11 we found less than 4 percent error. In the last test problem, after 263 hours, we stopped the solver.