Network-Based Optimization Models
Charles E. Noon, Ph.D.The University of Tennessee
Overview
What is a network? Common network-based models for logistics
– Shortest Path– Shortest Route– Service Area
Networks in a GIS An interconnected set of lines representing possible
paths from one location to another. A network structure is defined by arcs (lines) and
nodes (points). Their interaction is defined by topology.
Examples:– Road network– Shipping network– Railroad network– Air network
Basic Network-Based Optimization Models
1. Shortest Path2. Single Vehicle Shortest Route (or Tour)3. Service Area
Basic Prescriptive Modelsfor Transportation
1. Shortest Path (time or distance)
Basic Prescriptive Modelsfor Transportation
1. Shortest Path (time or distance)
2. Single Vehicle Shortest Route (or Tour)- aka Traveling Salesman Problem
Basic Prescriptive Modelsfor Transportation
1. Shortest Path (time or distance)
2. Single Vehicle Shortest Route (or Tour)- aka Traveling Salesman Problem
3. Service Area (time, distance or cost)
Session Overview Prescriptive Analysis Continued
1. Shortest Path2. Single Vehicle Shortest Route (or Tour)3. Service Area
Optimization Models4. Multi-Vehicle Routing5. Transportation Problem6. Facility Location
An Example
THE MODELING PROCESSModelDesign
Data Collectionand Analysis
Build Model
Validation
Optimization
Scenario Analysis
Conclusion
Geographic Information Systemsprovide a platform to
facilitate this process ...
… and bring the power of visualization to Implementation
Optimization Models Minimize or Maximize an Objective
– total system cost (prodn costs, whse costs, trans cost, inv cost)
– total profit– customer coverage– route time
Subject to Constraints– can be physical, financial, time– can be policy (inertia)
4. Multi-Vehicle Routing INPUTS:
– road network– point layer of demand locations with amounts– point layer of depots with capacitated vehicles– time info if desired (windows, stop, load, travel)
OUTPUTS:– assignment of demand points to depots– assignment of demand points to vehicle– route schedule
5. Transportation Problem INPUTS:
– road network– point layer of demand locations with amounts– point layer of supply locations with capacities
OUTPUTS:– transshipment flows from supply to demand
6. Facility Location Models INPUTS:
– point layer of existing and candidate facility locations– fixed cost for “opening” a facility– point layer of client locations– cost (or profit) of service matrix
OUTPUTS:– set of facilities which should be opened– assignment of clients to facilities
An Example
A distributor to fast-food restaurants with 12 DC’s serving 3922 restaurants with 80 vehicles.
Currently, DC’s serve from 209 to 644 restaurants.
TransCad was first used to determine optimal weekly delivery routes under the current restaurant-to-DC assignments.
CURRENT STORE-TO-DC ASSIGNMENTS
Total Mileage Per Week = 192,998
An Example A distributor to fast-food restaurants with 12 DC’s
serving 3922 restaurants with 80 vehicles. Currently, DC’s serve from 209 to 644 restaurants. TransCad was first used to determine optimal weekly
delivery routes under the current restaurant-to-DC assignments.
TransCad was then used to re-assign restaurants-to-DC’s and determine approximately 400 vehicle routes that must be run each week.
OPTIMIZED STORE-TO-DC ASSIGNMENTS
Total Mileage Per Week = 173,702
STORES WITH CHANGED ASSIGNMENTS
Note: a total of 381 stores had changed DC assignments. Each dot may represent more than one store (in the same zipcode)
STORES WITH CHANGED ASSIGNMENTS
CurrentlyAssignedDC
OptimallyAssigned
DC
Cluster
Net savings of 19,296 miles per week (10% reduction)