California Gasoline Transport

James Montgomery&

Karen Teague

Background

Williams Tank Lines is one of the largest for-hire bulk petroleum carriers in California (Fuel Transport Co.)

Founded by Michael Williams

Moving diesel and gasoline fuel to over 300 customers like the major gas stations you use everyday (ie.-Shell, Chevron, Arco, USA, etc.)

The company operates over 100 trucks out of 9 different terminal locations in California and 2 locations in Nevada.

This project focuses on 1 of the terminal locations2

Problem Statement

This project seeks to answer the following questions: What are the minimum number of trucks Mike needs in order to

full fill the normal network of Demands?

What are the effects of losing a refueling station at either Brisbane or San Jose?

What are the effects of losing individual refueling lanes?

How many 15 min traffic jams will keep Mike from delivering his loads in a 10 hour day?

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Overview

Fuel flow as a Min-Cost Flow Model

Goal: Make all deliveries at minimum cost (truck hours), satisfying all demand requirements

Key modifications to the basic model Unmet demands drives the flow (high penalty cost)

Add cost (nC=∞) for Unsatisfied Demand in the objective function we are minimizing

Because trucks make more than one delivery per day, a standard supply/demand network won’t work. All node demands are zero Demands tracked by flow over delivery arcs

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Overview

Measure of Effectiveness: Number of trucks needed to meet demands and total time to complete all deliveries

Assumptions: Time to every city and intersection = 15min. Interdictions begin after the 1st Time period

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Model Set-up(Parameters)

San Jose has 14 total trucks operating

All trucks start full and end empty in San Jose

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Fuel Demand

City Demand San Jose 37 Palo Alto 9 Menlo Park 9 San Mateo 8 San Bruno 6 San Francisco 30

Fuel Suppliers

San Jose (21) Brisbane (8)

Northern CA Gasoline Transport

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Model Set-up(Nodes)

Nodes Start, End Supply Cities, Demand Cities, Major Intersections Attached time layers (15min. Increments for a total of 10 hours)

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Start SJ2SJ1 ... SJ40 End

Model Set-up(Nodes)

Each City/Time Node is divided into two separate nodes: Full and Empty Represents a truck’s status upon entering the city

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StartSJ2E

SJ1E

...

...

SJ40E End

SJ2F

SJ1F

SJ40F

TIME PERIOD 1 TIME PERIOD 2 TIME PERIOD 3

Model Set-up(Arcs)

Between adjacent/same City nodes with concurrent time periods

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Exception Long Road Sections

SJ1F

PA1F

SJ1E

SJ2F

PA2F

SJ2E

SJ3F

PA3F

SJ3E

TIME PERIOD 1 TIME PERIOD 2 TIME PERIOD 3

Start

End

(100, 0, ∞)

Northern CA Gasoline Transport

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Model Set-up(Arcs)

Nodes can only connect to an adjacent node if they have the same Empty/Full Status

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Exceptions Delivery and Refueling Arcs

SJ1F

PA1F

PA1E

SJ2F

PA2F

PA2E

SJ3F

PA3F

PA3E

TIME PERIOD 1 TIME PERIOD 2 TIME PERIOD 3

Start

End

(100, 0, ∞)

Graphical Model for Demand

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Empty Nodes

PAE4

Demand

PAF2

PAE5PAF3

PAF4

(cij, 0, ∞)

1

3

1PAE6

+

+

= 9

* This is the onlyway to cross from the full network to the empty network.

Graphical Model for Refueling

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BACK INTO SYS

SanJE5 SanJF7

SanJE6 SanJF8

SanJE7 SanJF9

SanJF10SanJE8

}(SUM ≤ 21)} (SUM ≤ 21)

8+10+11+7 * This is the only

way to cross from the empty network to the full network.

Mathematical Model(caveman version)

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OBJ: min

s.t. Netflow constraintsDelivery RequirementsRefueling Limitations

Attack Scenario Notes

Problem is extremely computer intensive Extremely large number of possible solutions Costs for arcs approximately equal Delivery arcs are integer constrained

Primal and Dual objective values are suboptimal

Evaluate the data for trends rather than exact pivot points

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Scenarios

Baseline (no attacks) : What is the minimum number of trucks and the minimum cost to satisfy all demands?

Attack Scenario 1: What are the effects of losing an entire Refueling station for a time period?

Attack Scenario 2: What are the effects of losing individual refueling lanes at the refueling stations?

Attack Scenario 3: What are the effects or temporary traffic jams?

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Baseline (no attacks)

All demand satisfied – 13 trucks required Total Cost = 152 hours

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Attack Scenario 1

Attack Scenario 1: What are the effects of losing an entire Refueling station for a time period?

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Attack Scenario 1: Refueling Arcs

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1 Attack

X

Attack Scenario 1: Refueling Arcs

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2 Attacks

X2

Attack Scenario 1: Refueling Arcs

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3 Attacks

X

X2

Attack Scenario 1: Refueling Arcs

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4-7 Attacks

X4-7

Attack Scenario 1: Refueling Arcs

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8 Attacks

X7

X

Attack Scenario 1: Refueling Arcs

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9 Attacks

X8

X

Attack Scenario 1: Refueling Arcs

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10 Attacks

X4

X6

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Attack Scenario 1: Operator Resilience Curve

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Attack Scenario 1: Operator Resilience Curve

Attack Scenario 2

Attack Scenario 2: What are the effects of losing individual refueling lanes at the refueling stations?

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Attack Scenario 2: Refuel Lane Attacks

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1-8 Lanes Down

X8

Attack Scenario 2: Refuel Lane Attacks

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9 Lanes Down and Beyond

X8

X

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Attack Scenario 2: Operator Resilience Curve

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Attack Scenario 2: Operator Resilience Curve

Attack Scenario 3

Attack Scenario 3: What are the effects or temporary traffic jams closures?

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Attack Scenario 3: Road Arc Attacks

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1 – 15 minute traffic jam

X

Attack Scenario 3: Road Arc Attacks

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2 – 15 minute traffic jams

X

X

Attack Scenario 3: Road Arc Attacks

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3 - 15 minute traffic jams

X

XX

Attack Scenario 3: Road Arc Attacks

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4 - 15 minute traffic jams

X3X

Attack Scenario 3: Road Arc Attacks

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5 - 15 minute traffic jams

X3

XX

Attack Scenario 3: Road Arc Attacks

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6 - 15 minute traffic jams

X2X4

Attack Scenario 3: Road Arc Attacks

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7 - 15 minute traffic jams

X2

X

X3

X

Attack Scenario 3: Road Arc Attacks

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8 - 15 minute traffic jams

X4

X

X3

Attack Scenario 3: Road Arc Attacks

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9 - 15 minute traffic jams

X2

X

X6

Attack Scenario 3: Road Arc Attacks

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10 - 15 minute traffic jams

X2

X

X7

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Attack Scenario 3: Operator Resilience Curve

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Attack Scenario 3: Operator Resilience Curve

Summary & Conclusion

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System sensitive to changes in Refueling Lanes and Refueling Arcs, but robust against traffic jams.

Brisbane refueling capacity is the chokepoint

Future Work

Adding nodes and arcs Create full operations for San Jose Terminal

Includes deliveries on and refueling stations on the East side of the bay and deliveries south down the coast all the way to Santa Maria.

Add a second shift Create a problem specific algorithm or heuristic in

order to reduce run times to a manageable level.

What are the most efficient times to start shifts according to traffic congestions?

References

Dave Teague (Terminal Manager of San Jose branch): All Truck Data (cost of operations, routes, scheduling, etc.) Locations: refueling, demand cities

Googlemaps: http://maps.google.com/

Questions?

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