ISEN 601Location Logistics

Dr. Gary M. Gaukler

Fall 2011

SFMS with Rectilinear Distances

• Rectilinear distance:

• Total cost:

SFMS with Rectilinear Distances

• Properties of total cost function:

• Graph:

• Consequences:

SFMS with Rectilinear Distances

• Example 4.1:

SFMS with Rectilinear Distances

• Optimality properties:

SFMS with Rectilinear Distances

• Another example:

SFMS with Rectilinear Distances

Single Facility, Euclidean Distances

• Euclidean distance:

• lp-Norms:

Single Facility, Euclidean Distances

• Total cost function:

• Properties:

Single Facility, Euclidean Distances

• First order conditions:

Single Facility, Euclidean Distances• Compare with the “Varignon Frame”:

Single Facility, Euclidean Distances

• “Varignon Frame”, top view:

Single Facility, Euclidean Distances

• When does the system come to rest?

Single Facility, Euclidean Distances

• Majority Theorem:

Single Facility, Euclidean Distances

• Back to our optimality equations:

Single Facility, Euclidean Distances

• Iterative procedure:

Single Facility, Euclidean Distances

• When do we stop iterating?