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:

Node Optimality on GNs

Solving the 1-median Problem