ISEN 601 Location Logistics

ISEN 601Location Logistics

Dr. Gary M. GauklerFall 2011

Single Facility, Euclidean Distances• Total cost function:

• Properties:

Single Facility, Euclidean Distances• First order conditions:

Single Facility, Euclidean Distances• Iterative procedure:

Single Facility, Euclidean Distances• When do we stop iterating?

Single Facility, Euclidean Distances

Single Facility, Euclidean Distances

Single Facility, Euclidean Distances

Single Facility, Euclidean Distances

Single Facility, Euclidean Distances• Convex Hull property:

Single Facility, Euclidean Distances• Convex Hull property:

Single Facility, Euclidean Distances• Perturbed distance function:

Minimax Single Facility Model

Idea:

Applications:

Minimax with Euclidean Distances• Also known as Circle Covering Problem:

Minimax with Euclidean Distances• Mathematical formulation:

• Alternative formulation:

Algebraic Solution of Minimax• Recall problem formulation:

Algebraic Solution of Minimax• Equivalent problem:

Algebraic Solution of Minimax• Equivalent problem: