《土木与环境工程》（英文版） Logistical and Transportation Planning Methods

Location Theory II Logistical and Transportation Planning methods

Location Theory II Logistical and Transportation Planning Methods

Single tree Center Problem G is a tree.epi=1,2,…,m are the end vertices

Single Tree Center Problem G is a tree. ei, i=1,2,..., m are the end vertices

Single Tree Center Problem e Step1: Choose anyx∈G G is a tree. e. i=1. 2.m and find the end vertex are the end vertices say eN, farthest from x

Single Tree Center Problem eN Step 1: Choose any and find the end vertex, say eN, farthest from x. x ∈ G G is a tree. ei, i=1,2,..., m are the end vertices. x

Single tree center problem e N Step1: Choose any x∈G G is a tree. e i=1.2 and find the end vertex are the end vertices say eN, farthest from x Step 2: Find the end vertex say es, farthest from eN oe

Single Tree Center Problem eN Step 1: Choose any and find the end vertex, say eN, farthest from x. x ∈ G G is a tree. ei, i=1,2,..., m are the end vertices. Step 2: Find the end vertex, say e S, farthest from eN. x e S

Single tree center problem e N Step1: Choose any x∈G G is a tree. ei, i=1, 2 and find the end vertex are the end vertices say eN, farthest from x Step 2: Find the end vertex say es, farthest from eN Step 3: The absolute center of g is the midpoint of the path from en to es The vertex center is the vertex closest to that midpoint oe

Single Tree Center Problem eN x Step 2: Find the end vertex, say e S, farthest from eN. Step 3: The absolute center of G is the midpoint of the path from eN to e S. The vertex center is the vertex closest to that midpoint. Step 1: Choose any and find the end vertex, say eN, farthest from x. x ∈ G G is a tree. ei, i=1,2,..., m are the end vertices. e S

Single Tree center Problem e Step I: Choose any x∈G G is a tree e l- 1 and find the end vertex, are the end vertices say ex farthest from x Step 2: Find the end vertex say es, farthest from eN Step 3: The absolute center absolute center of g is the midpoint of the path from eN to es Vertex Center The vertex center is the vertex closest to that midpoint oe

Single Tree Center Problem eN x Step 2: Find the end vertex, say e S, farthest from eN. Step 3: The absolute center of G is the midpoint of the path from eN to e S. The vertex center is the vertex closest to that midpoint. Absolute center Vertex Center Step 1: Choose any and find the end vertex, say eN, farthest from x. x ∈ G G is a tree. ei, i=1,2,..., m are the end vertices. e S

Minimum manhattan distance Paths in the Presence of barriers Larson. Li etworks

Minimum Manhattan Distance Paths in the Presence of Barriers Larson, Li, Networks

o One of no O-D points / One of nB polygonal barriers

One of nQ O-D points One of nB polygonal barriers

9 One of no O-D points / One of nB polygonal barriers

One of nQ O-D points One of nB polygonal barriers

Communication The name of the game Two points having coordinates(x, y) and (u, V) COMMUNICATE if there exists at least one feasible staircase path between them Such a staircase path has minimum possible Manhattan length L(x2y)、(2)=x-u|+|y-v For example, any 2 adjacent vertices of a barrier communicate

Communication: The name of the game! • Two points having coordinates (x, y) and (u, v) COMMUNICATE if there exists at least one feasible staircase path between them. • Such a staircase path has minimum possible Manhattan length: • For example, any 2 adjacent vertices of a barrier communicate L[( x,y), ( u,v)] =| x − u | + | y − v |