Chapter 4 - Designing the Logistics Network

4/11/2019 CHAPTER 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 Contents • Graph and Network Optimization • Designing the Logistics Network • Models • Single-echelon Single-commodity Location Models (SESC) • Two-echelon Multi-commodity Location Models (TEMC) 4/11/2019 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 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)} 4/11/2019 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 or is adjacent to 7 is adjacent from/to or is adjacent from/to 4/11/2019 Graph and Network Optimization (7) • Path: A sequence of vertices that connects two nodes in a graph • A path from to is • The length of a path is the number of edges in the path Graph and Network Optimization (8) • Complete graph: A graph in which every vertex is directly connected to every other vertex 4/11/2019 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 SFO PVD ORD LGA HNL LAX DFW MIA 4/11/2019 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 • Length of a path is the sum of the weights of its edges • Example: Shortest path between Providence and Honolulu SFO PVD ORD LGA HNL LAX DFW MIA Graph and Network Optimization (12) Applications: • Package routing • Flight reservations • Driving directions Telephone routes Which communication links to activate when a user makes a phone call, e.g from Hong Kong to New York, USA Road systems design Problem: how to determine the number of lanes in each road? Given: expected traffic between each pair of locations Method: Estimate total traffic on each road link assuming each passenger will use shortest path 4/11/2019 Graph and Network Optimization (13) • Shortest Path Properties • Property 1: A subpath of a shortest path is itself a shortest path • Property 2: There is a tree of shortest paths from a start vertex to all the other vertices • Example: Tree of shortest paths from Providence PVD ORD SFO LGA HNL LAX DFW MIA GIẢI THUẬT TÌM ĐƯỜNG ĐI NGẮN NHẤT Mục tiêu bước lặp thứ n Tìm nút gần thứ n so với nút gốc (lặp lại với n = 1, 2, … nút gần nút đích) Đầu vào bước thứ n (n-1) nút gần với nút gốc (tìm từ bước lặp trước), bao gồm đường ngắn khoảng cách từ nút gốc Các ứng cử viên cho nút gần thứ n Mỗi nút xem xét có nối với nhiều nút chưa xem xét ứng cử viên Tính tốn nút gần thứ n Với nút xem xét ứng cử viên nó, cộng khoảng cách chúng với khoảng cách đường ngắn từ nút gốc đến nút xem xét  ứng cử viên có tổng khoảng cách ngắn nút gần thứ n 16 4/11/2019 VÍ DỤ - BÀI TỐN 17 VÍ DỤ - BÀI TỐN Nút khảo sát 18 4/11/2019 VÍ DỤ - BÀI TỐN Nút khảo sát 19 VÍ DỤ - BÀI TỐN  Tiếp tục bước lặp: 20  Đường ngắn nhất??? 10 ... E]* [13, D]* [ 14, E] [0, -] * [5, O] [4, A]* [5, C] [7, B]* [8, C] [9, D] [4, O]* [5, B] 27 VÍ DỤ – BÀI TOÁN [2, O]* [8, B]* [8, E]* [13, D]* [0, -] * [4, A]* [4, O]* [7, B]* 28 14 4/11/2019 BÀI... tất nút có nhãn cố định dừng 24 12 4/ 11/2019 VÍ DỤ – BÀI TOÁN [2, O] [0, -] * [5, O] [4, O] 25 VÍ DỤ – BÀI TỐN [2, O] [7, B] [0, -] * [5, O] [4, A] [4, O] [5, B] 26 13 4/ 11/2019 VÍ DỤ – BÀI TOÁN [2,... • Add to the cloud the vertex u outside the cloud with the smallest distance label, d(u) • Update the labels of the vertices adjacent to u Dijkstra’s Algorithm 16 4/ 11/2019 Graph and Network Optimization