Two optimal algorithms for finding bi-directional shortest path design problem in a block layout

In this paper, Shortest Path Design Problem (SPDP) in which the path is incident to all cells is considered. The bi-directional path is one of the known types of configuration of networks for Automated Guided Vehicles (AGV).To solve this problem, two algorithms are developed. For each algorithm an Integer Linear Programming (ILP) is determined. The objective functions of both algorithms are to find the shortest path. The path must be connected and incident to all cells at least in one edge or node. A simple Branch-and-Cut approach is used to solve the ILP models. Computational results show that the models easily can solve the problem with less than 45 cells using a commercial ILP solver.