Download - Multi-Commodity Flow Joe Monahan Josh Onuska
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Multi-Commodity Flow Joe MonahanJosh Onuska
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Back Story
• N.S. - Largest rail shipper of automobiles• Scope– Exclusive deal with Ford (1.9 million sold in 2010)– Facilities operating 24 hours / 7 days – East Coast distribution
• Risks– Terrorism or war– Labor union strikes– Severe weather– Derailing / rail failure
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Why Multi-Commodity?
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Nodes and Arcs
• Nodes– 5 assembly plants– 4 mixing centers– 25 distribution facilities
• Arcs– 22,000 miles of rail– 30,000 Ford vehicles shipped weekly– Capacity is more than sufficient to handle demand
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N.S. Rail System
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Automotive Shipping Facilities
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Assembly Plants & Mixing Centers
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Assembly PlantsLocation Supply Model
Cleveland 5,000 Econoline Van
Chicago 5,000 Taurus, Explorer
Detroit 10,000 Mustang, F-150, Focus
Kansas City 5,000 F-150, Escape, Contour
Louisville 5,000 SuperDuty,Expedition,Navigator
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Containerization
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Mixing Centers
Location Capacity RegionChicago 5938
NE/NWLouisville 3510
SE/EToledo 2800
NEKansas City 2538
NW/MW
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Chicago Mixing Center
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Node Overlay
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Node Overlay
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Model• Multi-commodity: Sorted (5) / Mixed• Supply/Demand Driven
– Supply = 30,000– Demand = 30,000– 60,000 units in motion– Accounts for 75% of Ford’s monthly U.S. sales
• Network Risks– Arcs unusable– Weather– Accident– Unions– Bridges
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Cleveland(Avon Lake)
Chicago
Detroit (Dearborn/Wayne)
Louisville
Kansas City
Toledo
Chicago
Louisville
Kansas City
Mixed SourceMixedSink
Assembly Plants
Mixing Stations
Assembly Sinks
-30,00030,000
-5000
-5000
-5000
-5000
-10000
D
C
L
K
A5000
5000
5000
5000
10000
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Network Characteristics• Network Goal– Meeting demand at the minimum cost– DNM: Current vs Future Profit loss
• Measure of effectiveness – Average cost to deliver vehicle to distribution
facility– MOE = Total Cost / # of cars shipped– Total Cost = (.25)(Rail Miles) + (DNM)($2700)
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Assumptions
• 30,000 cars moved per week (From Mid-West Plants)
– 20,000 to East Coast / 10,000 to West Coast• $0.25 per rail mile for each car moved • No cost incurred for movement between co-
located facilities• DNM results in lost sales
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Assembly Plants to Mixing Facilities
Mixing Facility
Assembly Plant
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Mixing Facilities to Distribution Sites
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Initial Results
• Base line – zero attacks:– Total Mileage: 25,511,500 Rail miles– Total Cost: $6,377,875.00– Cost per vehicle: $212.00
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Results w/ Interdiction
• 1 Interdiction– 23,219,000 Miles; $11,204,750; $386.37/car
• 5 Interdictions– 14,460,000 Miles; $49,515,000; $2,303.02/car
• 10 Interdictions– 8,010,000 Miles; $88,402,500; $6,314.46/car
• 17 Interdictions– 5,010,000 Miles; $139,600,500; $31,872.60/car
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Impacts of Interdiction
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.00
5,000,000.00
10,000,000.00
15,000,000.00
20,000,000.00
25,000,000.00
30,000,000.00
Rail Miles
Interdictions
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.00
10,000.00
20,000.00
30,000.00
40,000.00
50,000.00
60,000.00
Tot DNM
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Resiliency Curve
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.00
10,000.00
20,000.00
30,000.00
40,000.00
50,000.00
60,000.00
Demand Not Met & Cost
TotalMixedSortedCost/Car
Interdictions
Initial Attack Strategy
Detroit Taken Out
Attack Strategy switches
Cost over profit margin
Attack Saturation
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Charts: Cost of Interdiction
• Map of varying paths after each interdiction• And/or histograms of cost at each interdiction
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.00
5,000.00
10,000.00
15,000.00
20,000.00
25,000.00
30,000.00
35,000.00
Cost/Vehicle
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.00
50.00
100.00
150.00
200.00
250.00
300.00
350.00
Strict Cost/Vehicle
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Resiliency
• How do we make the system more robust and resistant to catastrophic collapse?– Add arcs to isolated nodes – Back up plan (trucks)
• Can we move nodes around (mixing stations or distribution points) to get a more efficient solution? – Moving or even eliminating mixing stations
improves performance.
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Optimal Attack Histogram
CHI-TOL
JAX-PAL
IND-CIN
STL-D
ES
FTW-CIN
FTW-IN
D
BIRM-MER
CHI-FTW
CHI-STL
KC-FTW
TOL-F
TWCHI-D
ES
LOU-ST
L
KC-DESKC-ST
L
LOU-LE
X
CIN-COL
LEX-KNOX
CLE-FTW
DET-FTW
DET-CHI
CLE-BUF
CLE-PIT
DET-TO
L
TOL-C
OL0
2
4
6
8
10
12
14
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Frequency of Attack Locations
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Additional Analysis
• Option to eliminate one of the four mixing facilities:– Bypassed Chicago– $194,375 in weekly savings
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Analysis Limitations
• Lots of assumptions• Changes in Consumer Demand by geographic
location
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Conclusion
• What did we learn from the model?– Hub and spoke affect
• How does the model react to interdiction?– Greatest impact from interdiction seen in DNM
• Critical vulnerabilities?– Isolated nodes, close proximity of Assm. Plants
• How can we improve the system to lower cost?– Eliminate Mixing Facility
• Diminishing returns after 17 attacks
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Questions