numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(fspp). the main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...

Path in a graph. The shortest path weight for a pair (u, v) of edges is defined as: δ(u, v) = ∞, if there is no path from u to v; δ(u, v) = min(w(p)): p connects u to v. A shortest path between u and v is any path p between them, such that w(p) = δ(u, v). Single-source shortest path problem. Given a graph G and a vertex v ∈ V , find the shortest path from v to every other node in the graph. Sin...

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 Vehi-cles (AGV).To solve this problem, two algorithms are developed. For each algorithm an Integer Linear Pro-gramming (ILP) is determined. The objective functions of both algorithms are t...