Sparse and Efficient Rebalancing Network Concentrating the Flows
Sparse and Efficient Rebalancing Network – Concentrating the Flows in Dynamic Network Chung-Piaw Teo NUS Business School Aaron Jinjia Huang, Mabel Chou, Institute of Operations Research and Analytics National University of Singapore Linfeng Li Hunan University
BIKE SHARING SYSTEM IS A POPULAR LAST MILE TRANSPORT SOLUTION IN MANY SMART CITIES NEW YORK BIKE SHARING SYSTEM HOW TO ENSURE AVAILABILITY OF BIKES TO RIDERS IN A COST EFFECTIVE WAY? Most frequent trip and rebalancing routes at 6 AM https: //medium. com/@Urbica. co/city-bike-rebalanced-92 ac 61 a 867 c 7
BIKE SHARING SYSTEM IS A POPULAR LAST MILE TRANSPORT SOLUTION IN MANY SMART CITIES Need to reposition workers and vehicles! Rebalancing Operation is COSTLY! Citi Bike rebalanced as many as 39, 811 bikes in February 2017, averaging 1, 422 bikes moves per day NEW YORK BIKE SHARING SYSTEM NEW YORK CITIBIKE: Total trips (blue) and total bike transfers x 10 (orange) hourly in 2015
How does the BSS operator incentivize user-based reposition ? - Match Spatiotemporal Supply and Demand • Operating 600 stations with over 10, 000 bikes and 55 neighborhoods • Rebalance over 1, 000 bicycle moves per day Figure 1. Hourly Bike Usage Pattern on Weekdays and Weekends In May 2016, Citi Bike launched a pilot program, called Bike Angels.
Citi Bike: Angel to Re-Balance Bikes • Angels earn points for taking bikes from crowded stations and bringing them to empty ones or stations expected to soon become empty. Rack up the points by cycling from a full station to an empty station. 1 st place wins $100, 2 nd place wins $75, 3 rd place wins $50, 4 th and 5 th place win $25. RANK ANGEL POINTS 1 AG 717 563 2 JT 249 404 3 JS 610 358 4 AB 705 346
How does the BSS operator incentivize user-based reposition ? - Match Spatiotemporal Supply and Demand Bike Angels Program • Two online maps provided to the users, one for the morning, and one for the afternoon • Station identification - Pick-Up station - Drop-Off Station - Neutral Station “Fixed pick-up/drop-off Structure” • Incentive Scheme - Members are encouraged to earn points following specific station-to-station patterns. - Volunteer deployment via historical usage information at each station. Figure 2 a. Static Map - Status of the stations are fixed for the AM and PM periods
How does the BSS operator incentivize user-based reposition ? - Match Spatiotemporal Supply and Demand Bike Angels Program • Dynamic map provided to the users in the realtime manner • Station identification - Pick-Up station - Drop-Off Station “Fully Flexible System” - Neutral Station • Incentive Scheme - Members are encouraged to earn points between any pair of stations. - Volunteer deployment via real-time bike usage at each station Figure 2 b. Dynamic Map - Status of the stations changes dynamically with actual usage
How does the BSS operator incentivize user-based reposition ? - Match Spatiotemporal Supply and Demand Fixed Pick-up/Drop-off Network • Predefined station-to-station pattern • Static Fully Flexible Network • Any pair of stations • Dynamic Adaptive Our goal is to find a simple sparse and static network structure so that it concentrates the real-time re-balancing flows in the network on “designated arcs” (i. e. , partially flexible system), and the expected loss in performance, compared to the dynamic adaptive (thus fully flexible) network, is only minimal.
Our Approach Earn rewards? • Sparse Network as Backbone to guide deployment • On-Line Deployment of Volunteers Earn Rewards
Effectivenss of the Sparse Network -Simulation Experiment Design Step 1 • 8 base stations are set up. • The net demand pattern of each base station follows prescribed distributions Step 2 Step 3 Step 4 • Generate 10, 000 samples • Each sample corresponds to one realized demand scenario for all 8 base stations. • For each realized demand scenario, we solve the maximum flow model under different structures (e. g. , Fully, Chaining and Sparse Structures) • Average the maximum flow value over 10, 000 samples, and obtain the samplepath performance Sparse structures are obtained by Dual-Variable-Based Heuristics
Effectivenss of the Sparse Network -Example 1 Figure 6. Chaining Structure Is Not Optimal Table 2. Sample-path Maximum Flow Performance for Structure beating 2 Chains • This example uses stations that are balanced in terms of usage. It is therefore difficult to pin-point the pick -up or the drop-off stations in this system. • The sparse structure obtained by our method outperforms other chain-like structure.
Effectivenss of the Sparse Network -Example 2 Figure 7. Fixed Pick-up/Drop-off Structure and 2 -Chain Structure in Balanced but Asymmetric System Table 3. Sample-path Maximum Flow Performance for Fixed Pick-up/Drop-off Structure and 2 -Chain Structure • The demand distributions exhibited in the last example are more prevalent in practice, due to the temporal and spatial pattern of bike usage in a city. • Interestingly, our heuristic recovers exactly the fixed pick-up/ drop-off structure for this example. It shows that the fixed pick-up/drop-off structure can outperform a 2 -chain structure in certain settings.
On-line Models: Deploying Volunteers via State-Dependent Policy 1 2
On-line Models: Deploying Volunteers via State-Dependent Policy 1 2
On-line Models: Deploying Volunteers via State-Dependent Policy 1 2
On-line Models: Deploying Volunteers via State-Dependent Policy
On-line Models: Deploying Volunteers via State-Dependent Policy
On-line Models: Deploying Volunteers via State-Dependent Policy Given the state-dependent heuristic, we would like to study the added advantage of concentrating rebalancing flows on suitably selected arcs in the sparse network (named partially flexible system) against the fully flexible system.
On-line Models: Deploying Volunteers via State. Dependent Policy Figure 8. 10 -Station Bike Sharing System with Prescribed Rider Trip Pattern Figure 9. Optimal 32 -arc Sparse Structure for the 10 -Station Bike Sharing System with Prescribed Rider Trip Pattern
On-line Models: Deploying Volunteers via State. Dependent Policy Figure 10. Average Performance Comparison between Sparse Solution and Fully Flexible Solution in Prescribed Rider Trip Case. The dotted lines on the left shows the no volunteer fullfillment number, and also the total number of riders ØWhen the volunteer arrival rate is reasonably large (0. 5 times of rider's arrival rate), we observe that the sparse solution outperforms the fully flexible solution in fulllfilling more rider demand (as many as 8%) with around 8. 5% reduction in rebalance moves.
Hubway Dataset Description Figure 11. Hubway Bicycle Sharing System, Boston Dataset Profile • The data for the Boston Hubway system spans around three months from May 1, 2012 to July 31, 2012. • Approximately 60 base stations in operations. • We partition the data into training and test sets: - the training set has 50 -weekday data from May 1 to July 9, - the test set has 16 -weekday data from July 10 to July 31. • AM denotes 7 : 00 -13 : 00, PM denotes 13 : 01 -20 : 00. • Including daily trip records, station id, user id, etc
Sparse Structure for Hubway BSS in Period AM --- Network design model (a) Arc number = 120 (a) Arc number = 240 (c) Arc number = 480 (a) Arc number = 720
Performance Comparison Table 8. In-sample and Out -sample Simulation Performance under Fully and Sparse Structure for Hubway BSS in Period AM
On-line Models: Deploying Volunteers via State. Dependent Policy Figure 12. State-dependent Algorithm Simulation Performance Comparison between Sparsity Solution and Fully Solution in Hubway BSS (480 arc) Ø Surprisingly, the static sparse structure facilitates the efficiency of on-line voluntary bike reposition policy in significantly reducing the total rebalance move for over 50% in comparison with fully structure regarding different volunteer availabilities, while performing nearly as well as the fully flexible system.
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