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California Gasoline Transport

This project evaluates the operational efficiency of Williams Tank Lines, a key petroleum carrier in California. It seeks to determine the minimum number of trucks required to meet fuel demands across various locations, assess the impact of losing refueling stations or lanes, and analyze how traffic congestion affects delivery schedules. By utilizing a Min-Cost Flow Model, the analysis aims to minimize delivery costs while ensuring all demands are satisfied. The findings will optimize trucking resources and enhance overall operational resilience.

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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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