James Montgomery amp Karen Teague Background Williams Tank Lines is one of the largest forhire bulk petroleum carriers in California Fuel Transport Co Founded by Michael Williams Moving diesel and gasoline fuel to over ID: 499378
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Slide1
California Gasoline Transport
James Montgomery
&
Karen TeagueSlide2
BackgroundWilliams
Tank Lines
is one of the largest for-hire bulk petroleum carriers in
California (Fuel Transport Co.)Founded by Michael WilliamsMoving 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 locations
2Slide3
Problem StatementThis 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?3Slide4
OverviewFuel 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 modelUnmet demands drives the flow (high penalty cost)Add cost (nC=∞) for Unsatisfied Demand in the objective function we are minimizingBecause trucks make more than one delivery per day, a standard supply/demand network won’t work.All node demands are zeroDemands tracked by flow over delivery arcs
4Slide5
OverviewMeasure 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 period5Slide6
Model Set-up(Parameters)San Jose has 14 total trucks operating
All trucks start full and end empty in San Jose
6
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)Slide7
Northern CA Gasoline Transport7Slide8
Model Set-up(Nodes)
Nodes
Start, End
Supply Cities, Demand Cities, Major IntersectionsAttached time layers (15min. Increments for a total of 10 hours) 8
Start
SJ2
SJ1
...
SJ40
EndSlide9
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
9
Start
SJ2
E
SJ1
E
...
...
SJ40
E
End
SJ2
F
SJ1
F
SJ40
F
TIME PERIOD 1
TIME PERIOD 2
TIME PERIOD 3Slide10
Model Set-up(Arcs)
Between adjacent/same City nodes with concurrent time periods
10
Exception
Long Road Sections
SJ1
F
PA1
F
SJ1
E
SJ2
F
PA2
F
SJ2
E
SJ3
F
PA3
F
SJ3
E
TIME PERIOD 1
TIME PERIOD 2
TIME PERIOD 3
Start
End
(100, 0, ∞)Slide11
Northern CA Gasoline Transport11Slide12
Model Set-up(Arcs)
Nodes can only connect to an adjacent node if they have the
same Empty/Full Status
12
Exceptions
Delivery and Refueling Arcs
SJ1
F
PA1
F
PA1
E
SJ2
F
PA2
F
PA2
E
SJ3
F
PA3
F
PA3
E
TIME PERIOD 1
TIME PERIOD 2
TIME PERIOD 3
Start
End
(100, 0, ∞)Slide13
Graphical Model for Demand
13
Empty Nodes
PAE
4
Demand
PAF2
PAE
5
PAF3
PAF4
(
c
ij
, 0, ∞)
1
3
1
PAE
6
+
+
= 9
* This is the only
w
ay to cross from the full network to the empty network. Slide14
Graphical Model for Refueling
14
BACK INTO SYS
SanJE5
SanJF7
SanJE6
SanJF8
SanJE7
SanJF9
SanJF10
SanJE8
}
(SUM ≤ 21)
}
(SUM ≤ 21)
8
+
10
+
11
+
7
* This is the only
w
ay to cross from the empty network to the full network. Slide15
Mathematical Model(caveman version)
15
OBJ:
min
s.t
.
Netflow
constraints
Delivery Requirements
Refueling Limitations
Slide16
Attack Scenario NotesProblem is extremely computer intensiveExtremely large number of possible solutions
Costs for arcs approximately equal
Delivery arcs are integer constrained
Primal and Dual objective values are suboptimalEvaluate the data for trends rather than exact pivot points
16Slide17
ScenariosBaseline (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?
17Slide18
Baseline (no attacks)All demand satisfied – 13 trucks requiredTotal Cost
= 152 hours
18Slide19
Attack Scenario 1Attack Scenario 1: What are the effects of losing an entire Refueling station for a time period?
19Slide20
Attack Scenario 1:
Refueling Arcs
20
1 Attack
XSlide21
Attack Scenario 1:
Refueling Arcs
21
2 Attacks
X2Slide22
Attack Scenario 1:
Refueling Arcs
22
3
Attacks
X
X2Slide23
Attack Scenario 1:
Refueling Arcs
23
4-7 Attacks
X4-7Slide24
Attack Scenario 1:
Refueling Arcs
24
8 Attacks
X7
XSlide25
Attack Scenario 1:
Refueling Arcs
25
9 Attacks
X8
XSlide26
Attack Scenario 1:
Refueling Arcs
26
10 Attacks
X4
X6Slide27
27
Attack Scenario 1
: Operator Resilience CurveSlide28
28
Attack Scenario 1
: Operator Resilience CurveSlide29
29
Attack Scenario 1
: Operator Resilience CurveSlide30
30
Attack Scenario 1
: Operator Resilience CurveSlide31
Attack Scenario 2Attack Scenario 2: What are the effects of losing individual refueling lanes at the refueling stations?
31Slide32
Attack Scenario 2:
Refuel Lane Attacks
32
1-8 Lanes
Down
X8Slide33
Attack Scenario 2:
Refuel Lane Attacks
33
9
Lanes Down and Beyond
X8
XSlide34
34
Attack Scenario 2:
Operator Resilience CurveSlide35
35
Attack Scenario 2:
Operator Resilience CurveSlide36
Attack Scenario 3Attack Scenario 3: What are the effects or temporary traffic jams closures?
36Slide37
Attack Scenario 3:
Road Arc Attacks
37
1 – 15 minute traffic jam
XSlide38
Attack Scenario 3:
Road Arc Attacks
38
2 – 15 minute traffic jams
X
XSlide39
Attack Scenario 3:
Road Arc Attacks
39
3 - 15 minute traffic jams
X
X
XSlide40
Attack Scenario 3:
Road Arc Attacks
40
4
- 15 minute traffic jams
X3
XSlide41
Attack Scenario 3:
Road Arc Attacks
41
5 - 15 minute traffic jams
X3
X
XSlide42
Attack Scenario 3:
Road Arc Attacks
42
6 - 15 minute traffic jams
X2
X4Slide43
Attack Scenario 3:
Road Arc Attacks
43
7 - 15 minute traffic jams
X2
X
X3
XSlide44
Attack Scenario 3:
Road Arc Attacks
44
8
- 15 minute traffic jams
X4
X
X3Slide45
Attack Scenario 3:
Road Arc Attacks
45
9
- 15 minute traffic jams
X2
X
X6Slide46
Attack Scenario 3:
Road Arc Attacks
46
10
- 15 minute traffic jams
X2
X
X7Slide47
47
Attack Scenario 3:
Operator Resilience CurveSlide48
48
Attack Scenario 3:
Operator Resilience CurveSlide49
Summary & Conclusion
49
System sensitive to changes in Refueling
Lanes and Refueling Arcs,
but robust against traffic jams
.
Brisbane refueling capacity is the chokepointSlide50
Future WorkAdding nodes and arcsCreate full operations for San Jose TerminalIncludes 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? Slide51
ReferencesDave Teague (Terminal Manager of San Jose branch):All Truck Data (cost of operations, routes, scheduling, etc.) Locations: refueling, demand citiesGooglemaps
:
http://maps.google.com
/ Slide52
Questions?
52