ISEN 601Location Logistics

Dr. Gary M. GauklerFall 2011

Heuristics• The myopic algorithm identifies the n median locations. • Customers are assigned to their closest median.• Improvement heuristic:

Myopic Example

Myopic Example

Improvement Example

Improvement Example

Improvement Example

Discrete Location Models

• “Warehouse Location Problem”

• p potential warehouse locations

Warehouse Location Problem

• Cost structure is more general:• Fixed costs

• Variable shipping/transportation costs

Warehouse Location Problem

• Decision variables:

Warehouse Location Problem

• Mixed-integer programming formulation:

Warehouse Location Problem• Heuristic algorithms:

• Add heuristic• Drop heuristic

Note that total cost generally decreases as facilities are added, and then increases after a point:

Warehouse Location Problem• Add heuristic:

Greedily add facilities to the solution until there is no facility to add that will reduce total cost

• Drop heuristic:Start with one facility at each candidate site. Remove facilities one by one until removal does not decrease total cost

Warehouse Location Problem• Example Add heuristic:

Warehouse Location Problem• Example Add heuristic:

Warehouse Location Problem• Example Add heuristic:

Warehouse Location Problem• Example Drop heuristic:

Warehouse Location Problem• Example Drop heuristic:

Transportation• Trends

Transportation• Some terms

• FTL:

• LTL:

Transportation• Transportation by type

Cost / ton-mile• Air: • FTL:• LTL:

Types of Transportation Paths

• Direct Shipment:

Direct Shipment

• Math formulation:

Direct Shipment

• When to use?

Improvements to Direct Shipment

• Option 1: Crossdocking

Improvements to Direct Shipment

• Option 2: DC

Improvements to Direct Shipment

• Option 3: Delivery rounds / TSP

Traveling Salesman Problem

• Problem statement:

Traveling Salesman Problem

• BIP formulation:

Traveling Salesman Problem• Subtours: