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)