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This document presents an analysis of the 2-Center Problem, highlighting its similarity to the covering problem, C(z). It discusses the conditions for the minimal objective function value of C(z) and the equivalence between C(z) and the 2-Center Problem, P1. Theoretical concepts are illustrated with practical examples, including a discussion on the n-Center Problem and algorithms related to location optimization on general networks. Key insights on median problems are also provided, making this a comprehensive resource for understanding location logistics.
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ISEN 601Location Logistics Dr. Gary M. Gaukler Fall 2011
2-Center Problem Alternative formulation (P1): Note:
2-Center Problem Looks almost like a covering problem! Consider the covering problem C(z): Note that for the 2-center case, the minimal objective function value of C(z) must be <=2
2-Center Problem Equivalence of C(z) and P1:
2-Center Problem Hence:
2-Center Problem Example:
2-Center Problem Example:
2-Center Problem Example:
2-Center Problem Example:
2-Center Problem Example:
n-Center Problem General approach:
n-Center Problem Algorithm:
n-Center Problem Algorithm:
Location on General Networks • Example:
Median Problem on GNs • Recall: node optimality for median problems
Node Optimality on GNs • Let’s look at a 1-median problem:
Node Optimality on GNs • Distances for the sample network:
