SIDT 2017 XXII SEMINARIO SCIENTIFICO DELLA SOCIETÀ ITALIANA DOCENTI DI TRASPORTI

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1 SIDT 2017 XXII SEMINARIO SCIENTIFICO DELLA SOCIETÀ ITALIANA DOCENTI DI TRASPORTI POLITECNICO DI BARI TOWARDS SUSTAINABLE CITIES: INNOVATIVE SOLUTIONS FOR MOBILITY AND LOGISTICS SEPTEMBER 14-15, 2017 SESSION G1-AM: SUSTAINABLE AND SMART MOBILITY User satisfaction based model for resource allocation in bike-sharing systems Leonardo Caggiani, Rosalia Camporeale, Mario Marinelli, Michele Ottomanelli

2 OVERVIEW Over the past decade, the number of ongoing bike-sharing programs has remarkably risen. Among their benefits, the reduction of congestion and emissions, the individual financial savings, the physical activity and their support for multimodal transport connections. STATION-BASED SYSTEMS predefined stations in which pick-up or drop-off the vehicles FREE-FLOATING SYSTEMS vehicles could be picked-up and parked in any spot, and not only at stations One of the main issues bike-sharing systems (BSS) may experiment is the potential lack of resources (i.e. bicycles and racks). Appropriate RESOURCE ALLOCATION in order to guarantee an efficient functioning and a reliable alternative to the other means of transportation.

3 WHAT HAS ALREADY BEEN DONE Several research methods have been proposed and developed aiming at optimizing the bike-sharing system design and operation: DESIGN DECISION VARIABLES: number of bikes, capacity and location of stations, vehicles repositioning... COMMON DEPENDENCIES: predicted user demand patterns, synergies between the BSS and the operating transit system, available budget... One of the main concern of public authorities is to maximize the benefits at the design and implementation stages, in order to make their investment as profitable as possible. What if the BSS has been already implemented? How to allocate a LIMITED amount of resources to ENHANCE its functioning?

4 STATEMENT OF THE PROBLEM The goal of this study is strategically enhance a BSS under a predefined available budget, even WITHOUT operate massive interventions on the actual system. OPTIMIZATION MODEL Spatio-temporal clusterization of the usage pattern data related to BSS stations. Maximization of the service quality of the system (i.e. user satisfaction). Calculation of the optimal number of racks/bikes to allocate in each station of an operating BSS. Applied to station-based realities, but easily adaptable to free floating ones.

5 SPATIO-TEMPORAL CLUSTERING METHOD Why it is necessary to operate a preliminary clusterization? We are usually dealing with a considerable amount of data (big data) related to the BSS, that we have to understand and analyze, in order to have a synthetic view of the information underlying the entire system, and to achieve its global enhancement. Each bike-sharing station has its own trend of available bicycles, that fluctuates during the time, collected at every time interval Δt. The maximum value that could be reached at every time step is equal to the total number of racks in that station (station completely full). On the contrary, if all the bicycles have been picked-up, no one is still available to use, and at that moment the collected number will be zero. After defined a significative period (Δz) of operation of the BSS, we can obtain a database with the number of available bicycles for each station, collected every Δt. These are the station temporal patterns that we propose to cluster/aggregate.

6 SPATIO-TEMPORAL CLUSTERING METHOD Knowing the temporal patterns associated with each station, and setting the total number of temporal clusters n, we can aggregate them according to their temporal trends. Discrete wavelets can de-noise and compress the signals, and are often used as a preprocessing step before clustering. Then, the filtered data are aggregated into a given number of temporal clusters Tk, applying a hierarchical clustering methodology (Caggiani et al., 2017). At the end of this procedure, each station belongs to a Tk. Next step aims at geographically aggregating groups of stations belonging to the same Tk, creating a certain number of spatio-temporal clusters Suk associated with each temporal one. This second clusterization has been done using a k-means algorithm. Every Suk has a maximum extension similar to the average distance that a user is willing to travel by walk, beginning the trip from his/her origin. We are assuming that, for any user, choose to pick-up a bicycle from one station rather than another (belonging to the same Suk) is totally equivalent.

7 ASSESSING THE PERFORMANCE OF A BSS How to measure the service quality of the system? The most accepted measures in literature seem to be those associated with two possible situations of unsatisfied demand: Zero-Vehicle Time (ZVT) & Full-Port Time (FPT) Kek et al. (2009) When ZVT occurs, the station has no available bicycles and users requests at that station will be rejected. When FPT occurs, the station has no empty racks and users requesting to return to that station will also fail. operator s point of view user s point of view Potential loss in revenue. Users forced to use other stations or turn to other modes of travel; additional usage costs.

8 OPTIMIZING THE SERVICE QUALITY OF A BSS The aim of the optimization consists in APPROPRIATELY ALLOCATING THE BIKE- SHARING RELATED RESOURCES (NAMELY, BICYCLES AND RACKS) with the main constraint of a given budget, in order to enhance its level of service. Analyzing the historical trends of available bicycles in each spatio-temporal cluster, we can calculate for how many time-intervals Δt the spatio-temporal clusters have no available bicycles (ZVTuk), or vice-versa, no available racks (FPTuk). The lowest is their value, the more efficiently the system is working. At the same time, it is also important to keep down the number of lost users of the system. Considering the actual behavior of the BSS, it is not possible to identify the exact number of unsatisfied users that the system loses, and THEN WE CONSIDER AS A PROXY ZVT AND FPT.

9 OPTIMIZING THE SERVICE QUALITY OF A BSS Supposing to change the number of racks and available bicycles at the beginning of the day in each spatio-temporal cluster, and assuming that the usage patterns are maintaining similar trends, we could GENERATE NEW LOST USERS and in the system: we have to minimize also their sum in order to guarantee the efficiency of the BSS. CURRENT STATUS SCENARIO 1

10 OPTIMIZING THE SERVICE QUALITY OF A BSS Supposing to change the number of racks and available bicycles at the beginning of the day in each spatio-temporal cluster, and assuming that the usage patterns are maintaining similar trends, we could GENERATE NEW LOST USERS and in the system: we have to minimize also their sum in order to guarantee the efficiency of the BSS. CURRENT STATUS SCENARIO 2

11 PROPOSED MODEL The decision variables are the optimal number of bicycles and racks to allocate in each spatio-temporal cluster subject to: SHIFT OF RACK NEW STATION Related to the available budget Consistency constraint

12 NUMERICAL APPLICATION: Test network We apply the suggested methodology to a station-based bike-sharing system test case. Study area (high density BSS): 1 kmq 36 bike-sharing stations with available bikes and racks Average walking distance for typical user: 500 m

13 NUMERICAL APPLICATION: Test network SPATIO-TEMPORAL CLUSTERIZATION OF BIKE-SHARING STATIONS 4 different typologies of bike-sharing stations: central, peripheral with a low demand request, peripheral with an average demand request, peripheral with a high demand request Stations temporal trends of available bicycles obtained thanks to the BSS simulator proposed by Caggiani and Ottomanelli (2012 and 2013) Δz = 14 days Δt = 5 min 4 temporal clusters Tk 11 spatio- temporal clusters Suk

14 NUMERICAL APPLICATION: Test network RESOURCES ALLOCATED IN EACH SPATIO-TEMPORAL CLUSTER Cluster ID Racks (starting values) Bicycles (starting values) New stations Cluster Racks New stations Cluster Bicycles New stations Unit costs of resources to allocate: BICYCLE COST= 100 ; RACK COST = 200 ; SHIFT COST = 100 ; NEW STATION COST = 300 ; TOTAL AVAILABLE BUDGET = Model thresholds: max 5 additional stations in every cluster; each station can have 5 to 15 racks; min 2 bicycles available at the beginning of an operation day (both in a new station and in each spatio-temporal cluster); max 5 new racks can be added in each cluster. The ZVT and FPT thresholds have been set equal to 0: this means that (respectively) one bicycle/one rack is reckoned sufficient to satisfy the users demand.

15 NUMERICAL APPLICATION: Test network RESOURCES ALLOCATED IN EACH SPATIO-TEMPORAL CLUSTER Cluster ID Racks (starting values) Bicycles (starting values) New stations Cluster Racks New stations Cluster Bicycles New stations Objective function value for the starting configuration (BEFORE resource allocation): 5934 Objective function value AFTER the resource allocation: 0 (this means that there are no timesteps with ZVT or FPT, neither expected lost users) 18 NEW BICYCLES 27 NEW RACKS 1 NEW STATION 9 RACK SHIFTS SPENDING 8400 (less than the available budget)

16 NUMERICAL APPLICATION: Test network SENSITIVITY ANALYSIS: AVAILABLE BUDGET AND ZVT/FPT THRESHOLD B = 1500 B = 2500 ξ = 0 ξ = 1 ξ = 2 ξ = 0 ξ = 1 ξ = 2 O.F. starting O.F. optimized best median O.F. starting O.F. optimized best median Tot. costs ( ) New bicycles best New racks (O.F.) Transfer racks B = 5000 B = ξ = 0 ξ = 1 ξ = 2 ξ = 0 ξ = 1 ξ = 2 O.F. starting O.F. optimized best median O.F. starting O.F. optimized best median Tot. costs ( ) New bicycles best (O.F.) New racks Transfer racks

17 NUMERICAL APPLICATION: Test network SENSITIVITY ANALYSIS: AVAILABLE BUDGET AND ZVT/FPT THRESHOLD B = 1500 B = 2500 ξ = 0 ξ = 1 ξ = 2 ξ = 0 ξ = 1 ξ = 2 O.F. starting O.F. optimized best median O.F. starting O.F. optimized best median Tot. costs ( ) New bicycles best New racks (O.F.) Transfer racks B = 5000 B = ξ = 0 ξ = 1 ξ = 2 ξ = 0 ξ = 1 ξ = 2 O.F. starting O.F. optimized best median O.F. starting O.F. optimized best median Tot. costs ( ) New bicycles best (O.F.) New racks Transfer racks

18 NUMERICAL APPLICATION: Test network SENSITIVITY ANALYSIS: AVAILABLE BUDGET AND ZVT/FPT THRESHOLD B = 1500 B = 2500 ξ = 0 ξ = 1 ξ = 2 ξ = 0 ξ = 1 ξ = 2 O.F. starting O.F. optimized best median O.F. starting O.F. optimized best median Tot. costs ( ) New bicycles best New racks (O.F.) Transfer racks B = 5000 B = ξ = 0 ξ = 1 ξ = 2 ξ = 0 ξ = 1 ξ = 2 O.F. starting O.F. optimized best median O.F. starting O.F. optimized best median Tot. costs ( ) New bicycles best (O.F.) New racks Transfer racks

19 NUMERICAL APPLICATION: Test network SENSITIVITY ANALYSIS: AVAILABLE BUDGET AND ZVT/FPT THRESHOLD B = 1500 B = 2500 ξ = 0 ξ = 1 ξ = 2 ξ = 0 ξ = 1 ξ = 2 O.F. starting O.F. optimized best median O.F. starting O.F. optimized best median Tot. costs ( ) New bicycles best New racks (O.F.) Transfer racks B = 5000 B = ξ = 0 ξ = 1 ξ = 2 ξ = 0 ξ = 1 ξ = 2 O.F. starting O.F. optimized best median O.F. starting O.F. optimized best median Tot. costs ( ) New bicycles best (O.F.) New racks Transfer racks

20 NUMERICAL APPLICATION: Real-size test network SPATIO-TEMPORAL CLUSTERIZATION OF BIKE-SHARING STATIONS Study area (high density BSS): 4 kmq 144 bike-sharing stations with available bikes and racks TOTAL AVAILABLE BUDGET = Δz = 28 days Δt = 5 min 4 temporal clusters Tk 33 spatio- temporal clusters Suk

21 NUMERICAL APPLICATION: Real-size test network MAIN RESULTS O.F. starting: O.F. optimized: 0 O.F. starting: O.F. optimized: 23 The convergence of the genetic algorithm used to perform the service level optimization is presented: setting a population of 50 and a maximum number of 1000 generations, the optimal solution is obtained after 429 generations. 107 NEW BICYCLES 4 NEW RACKS 4 NEW STATIONS 72 RACK SHIFTS SPENDING (the entire available budget)

22 CONCLUSIONS We are proposing a user satisfaction based model to allocate resources (bicycles and racks) in an operating BSS, in order to enhance its functioning under (primarily) a budget constraint. We suggest performing a preliminary spatio-temporal clusterization, that allows to reduce the amount of collected data, restituting a global and synthetic view of the functioning of the system. The optimization of the service quality of the BSS has been done from a user perspective. The achieved results are promising and seem to opportunely suggest the optimal way to invest the available budget granting a general improvement of the system. Although indirectly, this approach takes into account also the operator interests: assuring that ZVT and FTP are minimized, means at the same time that we are reducing the necessity to perform bicycle relocations in the system, essentially reducing the management costs of the BSS. Not secondarily, less lost users mean also a greater (potential) revenue.

23 THANKS FOR YOUR ATTENTION!