Reza Zanjirani Farahani - Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran. Supply Chain Management Research Center, Tehran, Iran.
Gilbert Laporte - Canada Research Chair in Distribution Management and GERAD, HEC Montréal, ۳۰۰۰ chemin de la Côte- Sainte-Catherine, Montreal, Canada H۳T ۲A۷.

In this article we present a mixed integer model that simultaneously can find the best single loop, direction of the loop and the location of P/D stations on the loop. The inputs of this model are block layout and from-to chart. The objective function is to minimize total travel time of AGVs. The constraints of the model are feasibility of loops, being P/D station of each cell on the edge(s) common between loop and the cell boundary. Feasibility of the loop means that the loop should be incident to at least one of the edges of each cell of a block layout. In our formulations we combine one of the recent algorithms used to determine shortest loop and a model that used to find the best location of P/D stations on a given loop. A compact formulation is developed for this problem and a relatively simple algorithm is resented. It is shown that instances containing up to 30 cells can be solved optimally using a commercial integer linear programming solver embedded within an iterative scheme.

AGV, Block Layout, Single Loop, P/D Stations, Mixed Integer Programming