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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

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California Gasoline Transport

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  1. California Gasoline Transport James Montgomery & Karen Teague

  2. 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 locations

  3. 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?

  4. 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

  5. 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

  6. Model Set-up(Parameters) • San Jose has 14 total trucks operating • All trucks start full and end empty in San Jose • Fuel Suppliers • Fuel Demand • San Jose (21) • Brisbane (8) • City Demand • San Jose 37 • Palo Alto 9 • Menlo Park 9 • San Mateo 8 • San Bruno 6 • San Francisco 30

  7. Northern CA Gasoline Transport

  8. Model Set-up(Nodes) • Nodes • Start, End • Supply Cities, Demand Cities, Major Intersections • Attached time layers (15min. Increments for a total of 10 hours) Start SJ40 End SJ1 SJ2 ...

  9. 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 TIME PERIOD 1 TIME PERIOD 2 TIME PERIOD 3 SJ1 F ... SJ40 F SJ2 F SJ40 E SJ1 E SJ2 E ... Start End

  10. Model Set-up(Arcs) • Between adjacent/same City nodes with concurrent time periods (100, 0, ∞) TIME PERIOD 1 TIME PERIOD 2 TIME PERIOD 3 Start SJ1 F SJ2 F SJ3 F PA1 F PA2 F PA3 F SJ1 E SJ2 E SJ3 E End • Exception • Long Road Sections

  11. Northern CA Gasoline Transport

  12. Model Set-up(Arcs) • Nodes can only connect to an adjacent node if they have the same Empty/Full Status (100, 0, ∞) TIME PERIOD 1 TIME PERIOD 2 TIME PERIOD 3 Start SJ1 F SJ2 F SJ3 F PA1 F PA2 F PA3 F PA1 E PA2 E PA3 E End • Exceptions • Delivery and Refueling Arcs

  13. Graphical Model for Demand Empty Nodes Demand (cij, 0, ∞) 1 3 1 PAF2 PAE4 * This is the only way to cross from the full network to the empty network. + + = 9 PAF3 PAE5 PAF4 PAE6

  14. Graphical Model for Refueling 8 + 10 + 11 + 7 } SanJE5 SanJF7 (SUM ≤ 21) BACK INTO SYS } SanJE6 SanJF8 (SUM ≤ 21) SanJE7 SanJF9 * This is the only way to cross from the empty network to the full network. SanJE8 SanJF10

  15. Mathematical Model(caveman version) OBJ: min s.t.Netflow constraints Delivery Requirements Refueling Limitations

  16. 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

  17. 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?

  18. Baseline (no attacks) • All demand satisfied – 13 trucks required • Total Cost = 152 hours

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

  20. Attack Scenario 1: Refueling Arcs 1 Attack X

  21. Attack Scenario 1: Refueling Arcs 2 Attacks X2

  22. Attack Scenario 1: Refueling Arcs 3 Attacks X X2

  23. Attack Scenario 1: Refueling Arcs 4-7 Attacks X4-7

  24. Attack Scenario 1: Refueling Arcs 8 Attacks X X7

  25. Attack Scenario 1: Refueling Arcs 9 Attacks X X8

  26. Attack Scenario 1: Refueling Arcs 10 Attacks X6 X4

  27. Attack Scenario 1: Operator Resilience Curve

  28. Attack Scenario 1: Operator Resilience Curve

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

  30. Attack Scenario 2: Refuel Lane Attacks 1-8 Lanes Down X8

  31. Attack Scenario 2: Refuel Lane Attacks 9 Lanes Down and Beyond X8 X

  32. Attack Scenario 2: Operator Resilience Curve

  33. Attack Scenario 2: Operator Resilience Curve

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

  35. Attack Scenario 3: Road Arc Attacks 1 – 15 minute traffic jam X

  36. Attack Scenario 3: Road Arc Attacks 2 – 15 minute traffic jams X X

  37. Attack Scenario 3: Road Arc Attacks 3 - 15 minute traffic jams X X X

  38. Attack Scenario 3: Road Arc Attacks 4 - 15 minute traffic jams X3 X

  39. Attack Scenario 3: Road Arc Attacks 5 - 15 minute traffic jams X3 X X

  40. Attack Scenario 3: Road Arc Attacks 6 - 15 minute traffic jams X2 X4

  41. Attack Scenario 3: Road Arc Attacks 7 - 15 minute traffic jams X X X2 X3

  42. Attack Scenario 3: Road Arc Attacks 8 - 15 minute traffic jams X3 X4 X

  43. Attack Scenario 3: Road Arc Attacks 9- 15 minute traffic jams X6 X2 X

  44. Attack Scenario 3: Road Arc Attacks 10- 15 minute traffic jams X7 X2 X

  45. Attack Scenario 3: Operator Resilience Curve

  46. Attack Scenario 3: Operator Resilience Curve

  47. Summary & Conclusion • System sensitive to changes in Refueling Lanes and Refueling Arcs, but robust against traffic jams. • Brisbane refueling capacity is the chokepoint

  48. 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?

  49. 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/

  50. Questions?

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