California Greyhound Bus Network

LT Catherine LongLT James Koffi

Agenda

Background Problem/Model Scenario Network Model Interdiction Takeaways/Further Research Summary/Conclusions Recommendations

Greyhound Bus Network

Greyhound serves more than 3,800 destinations in North America and employs around 7,800 staff.

Greyhound operated nearly 5.5 billion passenger miles last year.

The U.S. operation, as well as its operating subsidiaries and Greyhound Canada, carried nearly 18 million people.

Greyhound Bus Network

Intercity bus is the safest mode of transportation over cars, trucks, trains, planes and other commercial vehicles, according to the U.S. Department of Transportation

The Greyhound active fleet consists of about 1,775 buses, with an average age of 9.4 years.

One Greyhound bus takes an average of 19 cars off the road, and achieves 170 passenger miles per gallon of fuel.

Real World

Inside New Greyhound Bus

YouTube Video

http://www.youtube.com/watch?v=M_0Gz-Ie8T0&feature=channel&list=UL

Problem

The price of gas is expensive, and routes between stations vary throughout the state

New buses save gas and will keep up with the competition (Mega Bus, etc.)

What is the fastest and most cost effective way to transition 50 new express buses from two major Greyhound stations to other stations around the state of California?

Model Scenario

Model distributes 50 new buses throughout CA

Use GAMS to model the flow of buses to new stations and demonstrate how an “attack,” such as a major earthquake, impacts the network

The “attacks” model the worst case scenario and completely disable edge

Nodes and Arcs

The nodes in model represent stations

The arcs represent routes from one station to another

Route information is from the Greyhound website

Supply nodes are Oakland and Los Angeles

Road Map of California

Network Model

S

T

Network Model

S

Oakland

Los Angeles

T

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Measure of Effectiveness

The measure of effectiveness (MOE) for this model is to minimize the total cost of the flow of buses to their destination cities

Cost = $/gallon x miles per edge Each city besides the supply cities receives

2 brand new buses

Model Assumptions

Assume all new Greyhound buses get 6.5 miles per gallon

Cost per gallon of diesel is $4.00 Edge capacities are never exceeded

in our model

Greyhound Network Restrictions Many cities are connected by narrow two way roads which are

prohibited for use by Greyhound or any bus/motorhome in CA due to handling issues.

Bus: California Vehicle Code (CVC) Section 233 defines "bus" as: "(a) …any vehicle… …designed, used, or maintained for carrying more than 15 persons including the driver”

This is one of the major limitations to the network.

Operator’s/Attacker’s Problem

The model is run without interdiction to establish a baseline total minimum cost of $3,246.80

Run the model with increasing attacks to determine network resiliency

GAMS chooses routes that will maximize the total cost after each “attack”

Network ModelWith 1 Attack

S

Oakland

Los Angeles

T

Cost = 12624.404 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 2 Attacks

S

Oakland

Los Angeles

T

Cost = 17410.56 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 3 Attacks

S

Oakland

Los Angeles

T

Cost = 22061.208 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 4 Attacks

S

Oakland

Los Angeles

T

Cost = 31341.6012 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 5 Attacks

S

Oakland

Los Angeles

T

Cost = 36127.714 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 6 Attacks

S

Oakland

Los Angeles

T

Cost = 36581.8014 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 7 Attacks

S

Oakland

Los Angeles

T

Cost = 40844.8016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 8 Attacks

S

Oakland

Los Angeles

T

Cost = 41639.9016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 9 Attacks

S

Oakland

Los Angeles

T

Cost = 42023.9016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 10 Attacks

S

Oakland

Los Angeles

T

Cost = 42362.3016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 11 Attacks

S

Oakland

Los Angeles

T

Cost = 43136.5016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 12 Attacks

S

Oakland

Los Angeles

T

Cost = 43146.3016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Analysis

Can model resiliency be improved with an additional supply node in Bakersfield?

Yes, but it only changes the model slightly…

Network ModelWith 1 Attack

S

Oakland

Los Angeles

T

Cost = 12292.104 buses unable to reachOceanside and San Diego

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 2 Attacks

S

Oakland

Los Angeles

T

Cost = 17078.204 buses unable to reachOceanside and San Diego

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 3 Attacks

S

Oakland

Los Angeles

T

Cost = 21728.906 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 4 Attacks

S

Oakland

Los Angeles

T

Cost = 31009.3012 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 5 Attacks

S

Oakland

Los Angeles

T

Cost = 35795.3014 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 6 Attacks

S

Oakland

Los Angeles

T

Cost = 40512.5014 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 7 Attacks

S

Oakland

Los Angeles

T

Cost = 40512.5016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 8 Attacks

S

Oakland

Los Angeles

T

Cost = 40870.6016 buses unable to destination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 9 Attacks

S

Oakland

Los Angeles

T

Cost = 41094.6016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 10 Attacks

S

Oakland

Los Angeles

T

Cost = 41401.1016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 11 Attacks

S

Oakland

Los Angeles

T

Cost = 41759.2016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 12 Attacks

S

Oakland

Los Angeles

T

Cost = 41996.8016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 13 Attacks

S

Oakland

Los Angeles

T

Cost = 42043.6016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 14 Attacks

S

Oakland

Los Angeles

T

Cost = 42053.4016 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Operator’s Resilience Curve

Results

The most costly “attacks” occur with the first attack and the fourth attack Attack #1: 12624.40 - 3,246.80 =

$9377.60 Attack #4: 31341.60 - 22061.20 =

$9280.40

Network ModelWith 1 Attack

S

Oakland

Los Angeles

T

Cost = 12624.40Difference 12624.40 - 3,246.80 =9377.604 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 3 Attacks

S

Oakland

Los Angeles

T

Cost = 22061.208 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Network ModelWith 4 Attacks

S

Oakland

Los Angeles

T

Cost = 31341.60Difference = 31341.60 - 22061.20 = 9280.4012 buses unable to reachdestination

Santa Rosa

Santa Cruz

San Francisco

Santa Maria

San Luis Obispo

King City

Salinas

Stockton

San Diego

Indio

Sacramento

Vallejo

Modesto

Merced

Fresno

Bakersfield

Palmdale

Oceanside

Victorville

Indio

RiversideOxnard

Coalinga Jct

Los Banos

Santa Jose

Model Comparison

The additional supply station in Bakersfield decreased overall cost by $1,093.00 after 14 attacks

In the scenario with 3 supply stations Bakersfield started out by supplying just 4 new buses

By the 14th attack, Bakersfield supplies 14 buses

The more supply nodes the better, however may not be cost effective for Greyhound to have so many bus contracts

Future Analysis/Recommendations

Change the probability of destruction based on location, i.e. if on a fault line

Additional routes could be added to local roads and streets that connect the major interstates to build more redundancy in the network, but must abide to California state laws

Future Analysis/Recommendations

Model improvements can be achieved by increasing the granularity of the model

Can adapt the model to include other costs Price-tiered system Discounts on certain routes Express routes

Summary/Conclusions

We conclude there is not enough resiliency in the Greyhound network to sustain affordable bus transition operations in the event of “attacks” on the network depending on budget

Model can be used as a tool to weigh cost benefits of going around edges caused by a major traffic accident, or waiting an additional day for it to clear

Questions?

Sources

http://www.greyhound.com/en/about/factsandfigures.aspx

http://articles.latimes.com/2012/may/03/news/la-trb-greyhound-express-20120503