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 locations 2

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? 3

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 4

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 1 st Time period 5

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)

Northern CA Gasoline Transport 7

Model Set-up (Nodes)  Nodes Start, End Supply Cities, Demand Cities, Major Intersections Attached time layers (15min. Increments for a total of 10 hours) 8 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 9 Start SJ2 E SJ1 E... SJ40 E End SJ2 F SJ1 F SJ40 F TIME PERIOD 1TIME PERIOD 2TIME PERIOD 3

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 1TIME PERIOD 2TIME PERIOD 3 Start End (100, 0, ∞)

Northern CA Gasoline Transport 11

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 1TIME PERIOD 2TIME PERIOD 3 Start End (100, 0, ∞)

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

Graphical Model for Refueling 14 BACK INTO SYS SanJE5SanJF7 SanJE6SanJF8 SanJE7SanJF9 SanJF10SanJE8 } (SUM ≤ 21) } * This is the only way to cross from the empty network to the full network.

Mathematical Model (caveman version) 15

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 16

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? 17

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

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

Attack Scenario 1: Refueling Arcs 20 1 Attack X

Attack Scenario 1: Refueling Arcs 21 2 Attacks X2

Attack Scenario 1: Refueling Arcs 22 3 Attacks X X2

Attack Scenario 1: Refueling Arcs Attacks X4-7

Attack Scenario 1: Refueling Arcs 24 8 Attacks X7 X

Attack Scenario 1: Refueling Arcs 25 9 Attacks X8 X

Attack Scenario 1: Refueling Arcs Attacks X4 X6

27 Attack Scenario 1: Operator Resilience Curve

28 Attack Scenario 1: Operator Resilience Curve

29 Attack Scenario 1: Operator Resilience Curve

30 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? 31

Attack Scenario 2: Refuel Lane Attacks Lanes Down X8

Attack Scenario 2: Refuel Lane Attacks 33 9 Lanes Down and Beyond X8 X

34 Attack Scenario 2: Operator Resilience Curve

35 Attack Scenario 2: Operator Resilience Curve

Attack Scenario 3  Attack Scenario 3: What are the effects or temporary traffic jams closures? 36

Attack Scenario 3: Road Arc Attacks 37 1 – 15 minute traffic jam X

Attack Scenario 3: Road Arc Attacks 38 2 – 15 minute traffic jams X X

Attack Scenario 3: Road Arc Attacks minute traffic jams X X X

Attack Scenario 3: Road Arc Attacks minute traffic jams X3 X

Attack Scenario 3: Road Arc Attacks minute traffic jams X3 X X

Attack Scenario 3: Road Arc Attacks minute traffic jams X2 X4

Attack Scenario 3: Road Arc Attacks minute traffic jams X2 X X3 X

Attack Scenario 3: Road Arc Attacks minute traffic jams X4 X X3

Attack Scenario 3: Road Arc Attacks minute traffic jams X2 X X6

Attack Scenario 3: Road Arc Attacks minute traffic jams X2 X X7

47 Attack Scenario 3: Operator Resilience Curve

48 Attack Scenario 3: Operator Resilience Curve

Summary & Conclusion 49  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:

Questions? 52