Santander Cycles is a public bike-sharing scheme in London. There are more than 750 docking
stations and over 11,000 bikes in the system. Each station has a number of docks available
where bikes are stationed. A typical user would unlock a bike from a dock at the starting station,
ride the bike to the destination station, and park it into an available dock.
Due to imbalanced demand, the system would have full and empty docking stations over time,
making the access difficult. In order to maintaining the operations, rebalancing is needed. There
are two types of rebalancing: overnight rebalancing which decides the initial state of the system
into the daytime operation, and daytime rebalancing which balances the system during the
high-demanding hours. Vans are used to redistribute bikes by taking them from and loading
them to the stations. Each van can carry up to 30 bikes. We assume the van can start the
redistribution journey with any number (up to 30) of bikes.
The objective of the rebalancing is to minimize the total number of dissatisfied incidents,
defined as follows: If a customer who wants to use the bike cannot find any available one at a
station, there is one dissatisfied incident; if a customer who finishes the trip and wants to park
the bike into a station, but cannot find an available slot to park, there is one dissatisfied incident.
We would like you to design rebalancing strategy for the 8 stations in Hyde park area using
simulation. The rebalancing strategy consists of:
1. Decide the initial number of bikes for each station every morning.
2. For each van rebalancing trip, decide the starting time, the initial number of bikes on
the van and the route of redistribution (the sequence of visiting stations, and the loading
and unloading number at each station).
There are two data sets available:
1. The data set of each bike ride recorded in each day of a month, containing start station,
end station, start time, end time and duration (in seconds);
2. The data set containing the mean and standard deviation of traveling time between each
pair of stations by a van.
Assumptions and hints for the simulation:
1. Except for these 8 stations in Hyde park area, all other stations can be grouped into one
station with unlimited resources (i.e. unlimited bikes and available docks) as we are not
interested in designing strategy for those stations.
2. Customers would leave the starting station immediately if there is no bike available;
however, if there is no dock available to park the bike at the destination, they have to
wait for a dock to become available.
3. We assume the operating hours for those 8 stations are from 6:00 am to 10:00 pm. The
simulation should be a full cycle for the operating hours.
4. We assume the loading and unloading bikes from the van takes 15 seconds each.
5. The maximum number of redistribution trips per day is 2. In each trip, the van visits
each station at most once. The van can start at any station with arbitrary number (up to
30) of loaded bikes. It will then circulate among the stations to rebalance the bikes.
6. The arrival of the users can be modelled as Poisson processes and the arrival rate can
be estimated from the historical data.
7. When a user arrives at a station, the destination station can be decided based on a
probability distribution which you can draw from the historical data by calculating the
rate of each destination given a starting station.
8. It might be impossible to get the overall number of dissatisfied incidents to 0 under the
current constraints, your objective is to make it as smaller as possible.
The simulation framework based on SimPy is together with this assignment.
(a) (10 marks) For each (origin, destination) pair, in each hour, calculate the demand rates
based on the history data. Based on the rates, you can find probability distribution of the
destinations for a customer who starts from a given station. Only report the demand rates
and probabilities from Hyde Park Corner station to all other stations during 8-9 am.
(b) (10 marks) Based on the demand rates from (a), find the in-flow and out-flow of each station
during the morning rush hours (6-10 am) and afternoon rush hours (3-7 pm). For morning
and afternoon rush hours, identify the stations in Hyde Park area with the largest imbalance
(c) (10 marks) For each (origin, destination) pair, calculate the mean and standard deviation of
the time spend riding a bike based on the historical data. Only report the cycling times from
Hyde Park Corner station to all other stations.
(d) (10 marks) Based on (a) and (c), use Little’s law to find the average number of bikes on the
road during the 8-9 am and 1-2 pm respectively.
(e) (20 marks) In each trip, the van needs to visit all stations once and only once. Suppose we
ignore all the other constraints and set the objective as to minimize the total distance the
van travels in each trip. The starting point could be at any station. Formulate the problem
as Integer programming and find the optimal solution.
(f) (10 marks) Put your demand and service time estimation into the simulation code to simulate