Shared Car Network

1. Shared Car Network Production Scheduling Project – Spring 2014 Tyler Ritrovato (tr2397) Peter Gray (png2105)

2. The Idea • Google’s Driverless Car began design in 2005 and continues to advance • Advent of Uber and Lyft services in late 2000’s We see an opportunity… New Driverless Car Technology + Efficient Dispatching Algorithms __________________________ Shared Car Network

3. Shared Car Network • Instead of owning multiple cars per household, individuals or families become a member of a Shared Car Network (SCN) • Cars dispatched based on an efficient algorithm BENEFITS • Less cars on road is better for environment • Reduced traffic (at scale) • No more hassle of owning and maintaining personal cars RISKS • Not as flexible for on-demand trips • Potential for late or missed pick-ups

4. Relating to a Scheduling Problem • Machines  All the cars in the network • Regular Job  Picking up a customer and dropping that customer off. Defined by the following inputs: • Origin • Destination • Pick-up Time • Time due at destination • Processing Times: • Unoccupied Car  time from last drop-off to next customer pick-up • Occupied Car  time from pick-up of customer to drop-off

5. Optimization Decision Therefore, our problem boils down to the following production scheduling problem: P | rj , Lmax| m Minimize # of Machines # of Machines Constrain on Max Lateness and Minimum % of Requests Serviced Max Lateness % of Requests Serviced

6. Sample Data • Downloaded September, 2013 data from Citibike.com • Focused on the morning rush hour (8:00 AM- 10:00 AM) on Monday, September 9th. • Limited data to nine citibike ids (machines) • Release date  Start of trip • Due date  Trip Duration plus 20% • 24 Total Jobs

7. Algorithm Structure Utilizing a Greedy Algorithm: • Step 1: List job requests in ascending order (morning to night) • Step 2: For each job, choose the machine with the lowest metric score • Metric Score  Remaining processing time of current job + time to reach customer – time since availability • Add a machine if all of the possible machines lead to an undesirable lateness value • Step 3: Continue until all jobs are assigned

8. Algorithm Example • Job 1: Starts at 8:01 AM at W 25 St & 6 Ave and ends at 8:12 AM at Broadway & W 51 St • Add job 1 to machine 1

9. Algorithm Example • Job 2: Starts at 8:04 AM at 11 Ave & W 41 St and ends at 8:33 AM at John St & William St • Must add a second machine because using just machine 1 would lead to being late by 15 minutes • Lateness= 8 minutes remaining processing time from job 1 + 7 minutes to travel from job 1 ending point to job 2 starting point ✓ • Add job 2 to machine 2

10. Metric Score Example • Metric Score = Remaining processing time of current job + time to reach customer – time since availability • Job 11: Starts at 9:00AM at Fulton St and Grand Ave and ends at 9:04AM at Lafayette Ave and Classon Ave Machine 1: Available since 8:34 and is 24 ½ minutes away from pickup location  Metric Score = 0 + 24 ½ - 26 = -1 ½ Machine 2: Busy until 9:09 and is 11 minutes away  Metric Score = 9 + 11 - 0= 20 Machine 3: Busy until 9:07 and is 5 minutes away  Metric Score = 7 + 5 - 0 = 12 minutes away Machine 4: Available since 8:55 and is 33 minutes away  Metric Score = 0 + 33 - 5 = 28 Machine 5: Busy until 9:09 and is 0 minutes away  Metric Score = 9 + 0 - 0 = 9 • At this point in the algorithm, there are 5 machines • What machine should job 11 be assigned to? Machine 1

11. Gantt Chart

12. Results & Next Steps Results: • Citibike required 9 bikes needed for 24 job instances • Our shared car network algorithm required only 6 machines for 24 job instances • No late jobs • We service 100% of all requests Next Steps: • Try out our algorithm with more data (what happens when there are 100, 1000 jobs?) • Play with max lateness and % of requests serviced parameters to see affect on machine requirements • Create a program to compute algorithm

13. Questions? “General Solutions get you a 50% tip.” Source: xkcd.com