4. Motivations
• Growing demand for ride-sharing systems as a cost-effective
means of transportation
• Designing fundamental ride-sharing plans by solving various
scheduling problems
call
pick up
8. Method for optimization
• Let 𝑣 and 𝑟 be a model of vehicle and requests.
• Each 𝑡 has a vehicle and the requests that the vehicle
handles.
9. Method for optimization
• Penalty function
If 𝑟
𝑗 is not assigned because of lack of vehicles etc., much
cost will be given as penalty.
𝑗=1
𝑅
𝑐𝑝𝑒𝑛𝑎𝑙𝑡𝑦 ∙ 𝑥𝑗
where 𝑥𝑗 =
1 if 𝑥𝑗 is not assigned
0 otherwise
10. Method for optimization
Objective function: min 𝑘=1
𝑇
𝑐𝑘 ∙ 𝑡𝑘 + 𝑗=1
𝑅
𝑐𝑝𝑒𝑛𝑎𝑙𝑡𝑦 ∙ 𝑥𝑗
where 𝑡𝑘 =
1 if 𝑡𝑘 is chosen
0 otherwise
where 𝑥𝑗 =
1 if 𝑥𝑗 is not assigned
0 otherwise
Constrains:
∀𝑟
𝑗 ∈R, 𝑇𝑅
𝑡𝑘 + 𝑥𝑗 = 1, 𝑇𝑅 = {𝑘| 𝑡𝑘 is include 𝑟
𝑗}
∀𝑣𝑖 ∈V, 𝑇𝑉
𝑡𝑘 ≤ 1, 𝑉𝑉 = {𝑘| 𝑡𝑘 is include 𝑣𝑖}
13. References
[1] J. Alonso-Mora et al., “On-Demand High-Capacity Ride-
Sharing via Dynamic Trip-Vehicle Assignment”, PNAS,
114(3), 462-467, 2017. DOI: 10.1073/pnas.1611675114
Editor's Notes
「ライドシェアシステムにおける乗車要求への対話的車両割り当て」
Ridesharing is a means of transportation in which passengers designate where they want to get in and out of the vehicle, and the vehicle comes to them.
ライドシェアとは、乗客が乗り降りする場所を指定し、そこに車両がやってくるという交通機関である
Designing fundamental ride-sharing plans leads
I will explain the method for optimization simply.
:
A t does not consider all vehicle/request combinations.
A t is recorded as a vehicle/request combination only if a vehicle can handle requests under a threshold, or carpooling would not take too much time.
In addition, we consider a penalty function.
If 𝑟 𝑗 is not assigned because of lack of vehicles etc., much cost will be given as penalty.
Given these factors, the final optimization function looks like this.
Constrains represents that each vehicle and requests are chosen once.
Considering that a certain request is not chosen, in that case, xj takes 1, so that the sum is 1.
