California Gasoline Transport
description
Transcript of California Gasoline Transport
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
X2X
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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