Chapter 4 - Designing the Logistics Network.pdf

Chapter 4 - Designing the Logistics Network.pdf - CHAPTER 4...

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4/11/2019 1 DESIGNING THE LOGISTICS NETWORK DO NGOC HIEN TRAN QUOC CONG Industrial Systems Engineering Department Mechanical Engineering Faculty Ho Chi Minh City University of Technology - VNU CHAPTER 4 Contents Graph and Network Optimization Designing the Logistics Network Models Single-echelon Single-commodity Location Models (SESC) Two-echelon Multi-commodity Location Models (TEMC)

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4/11/2019 2 Graph and Network Optimization (1) What is a graph? A data structure that consists of a set of nodes (vertices) and a set of edges between the vertices. The set of edges describes relationships among the vertices. Graph and Network Optimization (2) Definitions Vertex: A node in a graph. Edge (arc): A pair of vertices representing a connection between two nodes in a graph. Undirected graph: A graph in which the edges have no direction. Directed graph (digraph): A graph in which each edge is directed from one vertex to another (or the same) vertex. Formally A graph G is defined as G = (V,E) where V(G) is a finite, nonempty set of vertices. E(G) is a set of edges written as pairs of vertices.
4/11/2019 3 Graph and Network Optimization (3) Undirected graph A graph in which the edges have no direction . The order of vertices in E is not important for undirected graphs. V(Graph1) = {A,B,C,D} E(Graph1) = {(A,B),(A,D),(B,C),(B,D)} Graph and Network Optimization (4) Directed graph A graph in which each edge is directed from one vertex to another (or the same) vertex The order of vertices in E is important for directed graphs. V(Graph2) = {1, 3, 5, 7, 9, 11} E(Graph2) = {(1,3), (3,1), (5,7), (5,9), (9,11), (9,9), (11,1)}

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4/11/2019 4 Graph and Network Optimization (5) Tree: A special case of directed graphs. V(Graph2) = {A, B, C, D, E, F, G, H, I, J} E(Graph2) = {(G,D), (G,J), (D,B), (D,F), (I,H), (I,J), (B,A), (B,C), (F,E)} Graph and Network Optimization (6) Graph terminology Adjacent vertices: Two vertices in a graph that are connected by an edge. 7 is adjacent from 5 or 5 is adjacent to 7 7 is adjacent from/to 5 or 5 is adjacent from/to 7 5 7 5 7
4/11/2019 5 Graph and Network Optimization (7) Path: A sequence of vertices that connects two nodes in a graph. A path from 1 to 4 is <1, 2, 3, 4>. The length of a path is the number of edges in the path. 1 2 3 4 Graph and Network Optimization (8) Complete graph: A graph in which every vertex is directly connected to every other vertex.

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4/11/2019 6 Graph and Network Optimization (9) Weighted graph Graph and Network Optimization (10) Weighted Graphs A graph for which each edge has an associated numerical value , called the weight of the edge . Edge weights may represent, distances, costs, etc. Example: in a flight route graph, the weight of an edge represents the distance in miles between the airports. ORD PVD MIA DFW SFO LAX LGA HNL
4/11/2019 7 Graph and Network Optimization (11) Shortest Path Problem Given a weighted graph and two vertices u and v , find a path of minimum total weight between u and v.

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• NguyenXuanLong,JohnLafferty

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