smart seminar series: improving public transport accessibility via the optimisation and...
TRANSCRIPT
![Page 1: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/1.jpg)
Synchronisation of Key Travel Modes
within a Transport Hub
Dr Michelle Dunbar
SMART Infrastucture Facility,
University of Wollongong
May 26, 2015
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 1/35
![Page 2: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/2.jpg)
Outline
Motivation for improving synchronisation in multi-modal transport.
Variations of the Vehicle Routing Problem (VRP).
A mathematical formulation for the VRPTW with heterogeneous
travellers.
Preliminary results.
Future directions + Application.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 2/35
![Page 3: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/3.jpg)
Motivation for Improved Synchronisation
In modern cities, transport infrastructure has typically developed according to a radial
pattern, in response to urban-sprawl.
Figure: Heatmap of population density in Sydney. Source: RP Data.
Population density increase may lead to inaccessibility to transportation services.
Infrastructure has traditionally developed separately and sequentially =⇒ lack of
complementarity and synchronisation between services at Hubs (△).
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 3/35
![Page 4: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/4.jpg)
Motivation for Improved Synchronisation
Passengers increasingly required to
make a number of interchanges at
Hubs, between different transport
modes.
Excessive waiting-times, infrequent
feeder services =⇒ poor connectivity.
Long-term planning and coordination: A
key driver for environmentally and
financially sustainable transport
development (Transport for NSW, 2012).
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 4/35
![Page 5: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/5.jpg)
Motivation for Improved Synchronisation
In areas without an existing transport infrastructure (such as an existing rail line),
buses are typically used to service the population.
- May be undesirable: fixed routes, infrequent services =⇒ increased car usage.
One approach commonly used around the
world, is that of a Dial-a-Ride shuttle-bus
system. (e.g. SkyBus in Melbourne)
Mobile technology has allowed for ease-of-use
and uptake for services to major Transport
Hubs.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 5/35
![Page 6: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/6.jpg)
The Vehicle Routing Problem
The Vehicle Routing Problem: Visit each node exactly once in minimal time.
Source: http://neo.lcc.uma.es/dynamic/vrp.html
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 6/35
![Page 7: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/7.jpg)
Existing Vehicle Routing Approaches
Vehicle Routing Problem (VRP), VRPTW (Vehicle Routing with Time Windows) and
DARP (Dial-a-Ride Problems).
1 Typically assume passengers/items are homogeneous w.r.t importance/priority,
2 Minimise total route time, cost or number of vehicles,
3 Solution approaches have typically utilised a combination of exact and heuristic
techniques (eg. tabu search),
4 Ignore the potential multi-modal aspect of a passenger’s trip.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 7/35
![Page 8: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/8.jpg)
Existing Vehicle Routing Approaches
Recent extensions include:
1 Multi-zone, multi-trip VRPTW to and from a
one or more depots (Crainic et al., 2012).
2 Heterogeneity of items and route-cost factors:
weight, volume, distance and number of stops.
(Cesseli et al., 2009.)
3 Exact solution techniques: Column generation.
(Ceselli et al., 2009)
4 Customer perceptions of quality of service:
waiting time at pick up node, trip length.
(Pacquette et al., 2013).
Figure 1: Example of a multi-zone, multi-trip solution.
vs
Figure 2: Non-Perishable vs Perishable items.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 8/35
![Page 9: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/9.jpg)
Contributions of Our Model
We extend the ideas of Ceselli et al. and Pacquette et al. Our approach:
1 Incorporates passenger heterogeneity with respect to value-of-time and importance of
outbound connection,
2 Minimises the time cost and missed connection cost,
3 Solved exactly via Column Generation.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 9/35
![Page 10: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/10.jpg)
Route-Based Formulation for the VRPTW
The VRPTW model may be formulated as a route-based model.
- Each route corresponds to a column of the coefficient matrix and has an
associated decision variable.
xr =
1, If route r is chosen,
0, otherwise.(1)
Example:
1
0
1
,
0
1
0
Passenger 1
Passenger 2
Passenger 3
Route 1 Route 2
s t1
2
3
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 10/35
![Page 11: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/11.jpg)
Route-Based Formulation for the VRPTW
The VRPTW model may be formulated as a route-based model.
- Each route corresponds to a column of the coefficient matrix and has an
associated decision variable.
xr =
1, If route r is chosen,
0, otherwise.(1)
Example:
1
0
1
,
0
1
0
Passenger 1
Passenger 2
Passenger 3
Route 1 Route 2
s t1
2
3x1 x2
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 10/35
![Page 12: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/12.jpg)
Route-Based Formulation for the VRPTW
The VRPTW model may be formulated as a route-based model.
- Each route corresponds to a column of the coefficient matrix and has an
associated decision variable.
xr =
1, If route r is chosen,
0, otherwise.(1)
Example:
1
0
1
,
0
1
0
Passenger 1
Passenger 2
Passenger 3
Route 1 Route 2
s t1
2
3x1 x2
s 1
3
t
Route 1
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 10/35
![Page 13: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/13.jpg)
Route-Based Formulation for the VRPTW
The VRPTW model may be formulated as a route-based model.
- Each route corresponds to a column of the coefficient matrix and has an
associated decision variable.
xr =
1, If route r is chosen,
0, otherwise.(1)
Example:
1
0
1
,
0
1
0
Passenger 1
Passenger 2
Passenger 3
Route 1 Route 2
s t1
2
3x1 x2
s
2
t
Route 2
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 10/35
![Page 14: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/14.jpg)
Column Generation
Master Problem Subproblem
1 0 0
1 0 0
0 1 0
1 0 0
0 1 0
0 0 1
x=
1
1
1
1
1
1
z = c1x1 + c2x2 + c3x3
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 11/35
![Page 15: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/15.jpg)
Column Generation
Master Problem Subproblem
1 0 0
1 0 0
0 1 0
1 0 0
0 1 0
0 0 1
x=
1
1
1
1
1
1
z = c1x1 + c2x2 + c3x3 Generate Column
1
0
1
0
0
1
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 11/35
![Page 16: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/16.jpg)
Column Generation
Master Problem Subproblem
1 0 0 1
1 0 0 0
0 1 0 1
1 0 0 0
0 1 0 0
0 0 1 1
x=
1
1
1
1
1
1
z = c1x1 + c2x2 + c3x3 + c4x4
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 11/35
![Page 17: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/17.jpg)
Column Generation
Master Problem Subproblem
1 0 0 1
1 0 0 0
0 1 0 1
1 0 0 0
0 1 0 0
0 0 1 1
x=
1
1
1
1
1
1
z = c1x1 + c2x2 + c3x3 + c4x4 Generate Column
0
1
0
1
1
0
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 11/35
![Page 18: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/18.jpg)
Column Generation
Master Problem Subproblem
1 0 0 1 0
1 0 0 0 1
0 1 0 1 0
1 0 0 0 1
0 1 0 0 1
0 0 1 1 0
x=
1
1
1
1
1
1
z = c1x1 + c2x2 + c3x3 + c4x4 + c5x5
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 11/35
![Page 19: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/19.jpg)
Column Generation
Master Problem Subproblem
1 0 0 1 0
1 0 0 0 1
0 1 0 1 0
1 0 0 0 1
0 1 0 0 1
0 0 1 1 0
x=
1
1
1
1
1
1
z = c1x1 + c2x2 + c3x3 + c4x4 + c5x5
Terminate if we can find no other
beneficial columns.
(i.e. All reduced costs, cj ≥ 0)
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 11/35
![Page 20: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/20.jpg)
Solving the VRPTW using Column Generation
Objective is to obtain a minimal time-cost assignment of available vehicles to
passenger pick-ups, ensuring each passenger is picked up within their specified
time-window.
Master Problem
Minimise :
∑
r∈R
crxr
Subject to :∑
r∈R
airxr = 1 ∀i ∈ N
∑
r∈R
xr ≤ N, xr ∈ {0, 1}
Subproblem
Generate a feasible vehicle
route (satisfying time window
and duration constraints).
Append to the set:
R = set of all possible routes.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 12/35
![Page 21: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/21.jpg)
Route-Based VRPTW with Passenger Heterogeneity
Objective is minimise both time cost and missed (outbound) connection cost
at the Transport Hub, whilst ensuring each passenger is picked up within their
specified time window.
Master Problem
Minimise :
∑
r∈R
(
cr + λcMr)
xr
Subject to :∑
r∈R
airxr = 1 ∀i ∈ N
∑
r∈R
xr ≤ N, xr ∈ {0, 1}
Subproblem
Generate a feasible vehicle
route (satisfying time window
and duration constraints).
Append to the set:
R = set of all possible routes.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 13/35
![Page 22: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/22.jpg)
Subproblem
A Label-Setting algorithm is used to determine the path with minimal reduced cost:
- Let π denote a path from source to sink.
- Let ti be the time-cost incurred by travelling from the predecessor node π−(i) to node i.
- Let wi be the dual multiplier for node i.
- Let li and ui denote the lower and upper bounds of the time window for node i.
Subproblem Formulation
Minimise : λcMr +∑
i∈π
(ti − wi)
Subject to: li ≤∑
i∈π(i)
ti ≤ ui, ∀i ∈ N .
∑
i∈π
ti ≤ Tmax, ∀i ∈ N
π is a path from s to t.
Where: cr =∑
i∈πti, Time Cost
cMr
=∑
i∈πmax{pi(cr−di),0}, MC.Cost.
s t
1
23
4
5
6
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 14/35
![Page 23: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/23.jpg)
Subproblem
A Label-Setting algorithm is used to determine the path with minimal reduced cost:
- Let π denote a path from source to sink.
- Let ti be the time-cost incurred by travelling from the predecessor node π−(i) to node i.
- Let wi be the dual multiplier for node i.
- Let li and ui denote the lower and upper bounds of the time window for node i.
Subproblem Formulation
Minimise : λcMr +∑
i∈π
(ti − wi)
Subject to: li ≤∑
i∈π(i)
ti ≤ ui, ∀i ∈ N .
∑
i∈π
ti ≤ Tmax, ∀i ∈ N
π is a path from s to t.
Where: cr =∑
i∈πti, Time Cost
cMr
=∑
i∈πmax{pi(cr−di),0}, MC.Cost.
s t
1
23
4
5
6s
1
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 14/35
![Page 24: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/24.jpg)
Subproblem
A Label-Setting algorithm is used to determine the path with minimal reduced cost:
- Let π denote a path from source to sink.
- Let ti be the time-cost incurred by travelling from the predecessor node π−(i) to node i.
- Let wi be the dual multiplier for node i.
- Let li and ui denote the lower and upper bounds of the time window for node i.
Subproblem Formulation
Minimise : λcMr +∑
i∈π
(ti − wi)
Subject to: li ≤∑
i∈π(i)
ti ≤ ui, ∀i ∈ N .
∑
i∈π
ti ≤ Tmax, ∀i ∈ N
π is a path from s to t.
Where: cr =∑
i∈πti, Time Cost
cMr
=∑
i∈πmax{pi(cr−di),0}, MC.Cost.
s t
1
23
4
5
6s
1
2
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 14/35
![Page 25: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/25.jpg)
Subproblem
A Label-Setting algorithm is used to determine the path with minimal reduced cost:
- Let π denote a path from source to sink.
- Let ti be the time-cost incurred by travelling from the predecessor node π−(i) to node i.
- Let wi be the dual multiplier for node i.
- Let li and ui denote the lower and upper bounds of the time window for node i.
Subproblem Formulation
Minimise : λcMr +∑
i∈π
(ti − wi)
Subject to: li ≤∑
i∈π(i)
ti ≤ ui, ∀i ∈ N .
∑
i∈π
ti ≤ Tmax, ∀i ∈ N
π is a path from s to t.
Where: cr =∑
i∈πti, Time Cost
cMr
=∑
i∈πmax{pi(cr−di),0}, MC.Cost.
s t
1
23
4
5
6s
1
2
4
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 14/35
![Page 26: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/26.jpg)
Subproblem
A Label-Setting algorithm is used to determine the path with minimal reduced cost:
- Let π denote a path from source to sink.
- Let ti be the time-cost incurred by travelling from the predecessor node π−(i) to node i.
- Let wi be the dual multiplier for node i.
- Let li and ui denote the lower and upper bounds of the time window for node i.
Subproblem Formulation
Minimise : λcMr +∑
i∈π
(ti − wi)
Subject to: li ≤∑
i∈π(i)
ti ≤ ui, ∀i ∈ N .
∑
i∈π
ti ≤ Tmax, ∀i ∈ N
π is a path from s to t.
Where: cr =∑
i∈πti, Time Cost
cMr
=∑
i∈πmax{pi(cr−di),0}, MC.Cost.
s t
1
23
4
5
6s
1
2
4
6
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 14/35
![Page 27: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/27.jpg)
Subproblem
A Label-Setting algorithm is used to determine the path with minimal reduced cost:
- Let π denote a path from source to sink.
- Let ti be the time-cost incurred by travelling from the predecessor node π−(i) to node i.
- Let wi be the dual multiplier for node i.
- Let li and ui denote the lower and upper bounds of the time window for node i.
Subproblem Formulation
Minimise : λcMr +∑
i∈π
(ti − wi)
Subject to: li ≤∑
i∈π(i)
ti ≤ ui, ∀i ∈ N .
∑
i∈π
ti ≤ Tmax, ∀i ∈ N
π is a path from s to t.
Where: cr =∑
i∈πti, Time Cost
cMr
=∑
i∈πmax{pi(cr−di),0}, MC.Cost.
s t
1
23
4
5
6s
1
2
4
6 t
110101
Route Cost = cr + λcMr
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 14/35
![Page 28: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/28.jpg)
Preliminary Numerical Results
We randomly generated 4 different datasets with characteristics reflecting ‘likely’
passenger compositions according to time-of-day requests.
- School commute (≈ 8am/3pm),
- Balanced number of requests (≈ 11am/2pm),
- Inter-city commute (≈ 7am/5pm),
- Business commute (≈ 6am/6pm).
For each of these datasets, we simulated 10 random instances with different passenger
outbound connection departure times at the Hub, to determine the effectiveness of our
algorithm.
Each dataset consists of 30 passengers, with the restriction that vehicles must return to
the Hub in <= 20 mins.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 15/35
![Page 29: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/29.jpg)
Preliminary Numerical Results
In the slides that follow, we compare:
- The Base Case (Min TTT): Objective is to minimise Total Travel Time (TTT).
- Our Model (Min TTT+MC): Objective is to minimise Total Travel Time and Missed
Connection Cost.
We compare the following quantities:
- Time Cost,
- Missed Connection Cost,
- Time Cost + Missed Connection Cost (weighted),
- Total Cost (includes additional vehicle cost ($40/20 min), if required).
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 16/35
![Page 30: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/30.jpg)
Results: School (5,5,15,5)
−5 −4 −3 −2 −1 0 1 2 3 4 5−5
−4
−3
−2
−1
0
1
2
3
4
5
Distance (kms)
Distance(kms)
Plot of the Vehicle Routing Solution(Obj: Minimise Total Travel Time): Using 6 vehicles.
1
2
3
1021
25
5
14
16
18
23
30
67
8
22
24
27
28
29
413
15
19
9
11
17
26
1220
Total Travel Time Cost = 89,
Missed Connections = 4,
Missed Connection Cost = 310,
Weighted Cost Sum = 244.
Hub Aircraft Connection: 5 Inter−city Train Connection: 5 Bus Connection: 15 Walk Connection: 5
−5 −4 −3 −2 −1 0 1 2 3 4 5−5
−4
−3
−2
−1
0
1
2
3
4
5
Distance (kms)
Distance(kms)
Plot of the Vehicle Routing Solution(Obj: Minimise Total Travel Time and Missed Connection Cost): Using 6 vehicles.
9
11
17
67
8
22
24
27
28
29
2
3
1021
23
30
1
413
15
19
1220
25
5
14
16
18
26
Total Travel Time Cost = 90,
Missed Connections = 0,
Missed Connection Cost = 0,
Weighted Cost Sum = 90.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 17/35
![Page 31: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/31.jpg)
Results: Balanced (10,10,10,0)
−5 −4 −3 −2 −1 0 1 2 3 4 5−5
−4
−3
−2
−1
0
1
2
3
4
5
Distance (kms)
Distance(kms)
Plot of the Vehicle Routing Solution(Obj: Minimise Total Travel Time): Using 7 vehicles.
1
6
12
19
28
29
3
11
15
17
18
21
26
5
14
25
30
4
13
16
27
2
20
9
10
22
23
24
7
8
Total Travel Time Cost = 86,
Missed Connections = 3,
Missed Connection Cost = 850,
Weighted Cost Sum = 511.
Hub Aircraft Connection: 10 Inter−city Train Connection: 10 Bus Connection: 10
−5 −4 −3 −2 −1 0 1 2 3 4 5−5
−4
−3
−2
−1
0
1
2
3
4
5
Distance (kms)
Distance(kms)
Plot of the Vehicle Routing Solution(Obj: Minimise Total Travel Time and Missed Connection Cost): Using 8 vehicles.
141
12
19
28
29
7
25
30
2
20
8
9
10
22
23
243
6
26
5
13
16
17214
11
1518
27
Total Travel Time Cost = 104,Missed Connections = 1,
Missed Connection Cost = 40,
Weighted Cost Sum = 124(164).
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 18/35
![Page 32: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/32.jpg)
Results: Inter-city Commute (5,20,5,0)
−5 −4 −3 −2 −1 0 1 2 3 4 5−5
−4
−3
−2
−1
0
1
2
3
4
5
Distance (kms)
Distance(kms)
Plot of the Vehicle Routing Solution(Obj: Minimise Total Travel Time): Using 6 vehicles.
6
12
18
30
9
11
15
16
26
2
14
21
22
23
13
17
25
3
5
10
28
14
78
1920 24
27
29
Total Travel Time Cost = 86,Missed Connections = 3,
Missed Connection Cost = 525,
Weighted Cost Sum = 348.5.
Hub Aircraft Connection: 5 Inter−city Train Connection: 20 Walk Connection: 5
−5 −4 −3 −2 −1 0 1 2 3 4 5−5
−4
−3
−2
−1
0
1
2
3
4
5
Distance (kms)
Distance(kms)
Plot of the Vehicle Routing Solution(Obj: Minimise Total Travel Time and Missed Connection Cost): Using 7 vehicles.
1920 24
29
3
5
10
17
13
25
28
2
14
21
22
23
9
11
15
16
26
6
12
18
30
14
7827
Total Travel Time Cost = 94,Missed Connections = 0,
Missed Connection Cost = 0,
Weighted Cost Sum = 94(134).
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 19/35
![Page 33: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/33.jpg)
Results: Business (15,10,5,0)
−5 −4 −3 −2 −1 0 1 2 3 4 5−5
−4
−3
−2
−1
0
1
2
3
4
5
Distance (kms)
Distance(kms)
Plot of the Vehicle Routing Solution(Obj: Minimise Total Travel Time): Using 6 vehicles.
1
6
10
22
27
816 18
21
29
5
13
23
24
25
3
9
12
17
19
2
4 14
1528
7
1120
26
30
Total Travel Time Cost = 88,
Missed Connections = 3,
Missed Connection Cost = 320,
Weighted Cost Sum = 248.
Hub Aircraft Connection: 15 Inter−city Train Connection: 10 Bus Connection: 5
−5 −4 −3 −2 −1 0 1 2 3 4 5−5
−4
−3
−2
−1
0
1
2
3
4
5
Distance (kms)
Distance(kms)
Plot of the Vehicle Routing Solution(Obj: Minimise Total Travel Time and Missed Connection Cost): Using 8 vehicles.
1
6
26
810
22
27
2
4 14
18
29
315
21
28
5
13
23
24
25
1120
30
9
12
17
19
7
16
Total Travel Time Cost = 90,
Missed Connections = 0,
Missed Connection Cost = 0,
Weighted Cost Sum = 90(170).
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 20/35
![Page 34: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/34.jpg)
Average Costs for each Dataset over 10 Random Instances
Dataset
TotalCost
($)
A Comparison of the Average Total Costs between Min TTT and Min TTT+MC over 10 Instances for each Dataset
School Balanced Inter−City Business0
50
100
150
200
250
300
350
400
450
Time Cost (Min. TTT)
Missed Connection Cost (Min. TTT)
Additional Vehicle/Driver Cost (Min. TTT)
Time Cost (Min. TTT+MC)
Missed Connection Cost (Min. TTT+MC)
Additional Vehicle/Driver Cost (Min. TTT+MC)
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 21/35
![Page 35: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/35.jpg)
Results: Average Percentage Improvement
Average percentage improvement of Min TTT+MC over the Min TTT approach.
Travel Cost MC Cost Weighted Sum Total Cost
School -1.35 100.00 55.67 55.67
Balanced -11.16 94.75 59.38 45.40
Inter-City -8.49 100.00 57.10 36.87
Business -6.705 95.41 73.76 57.37
Average -6.93 97.54 61.48 48.83
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 22/35
![Page 36: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/36.jpg)
Remarks and Conclusions
Using the same number of vehicles, it is possible to obtain a route with a 100%
decrease in missed connection cost, for only a 1.3% increase in time cost.
Over all 4 dataset types, the average reduction in missed connection cost was
between 94− 100%.
Over all 4 dataset types, the Min TTT+MC approach outperformed the Min TTT
approach, even when (≤ 2) additional vehicles costs are accounted for, by an
average of 48.83%
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 23/35
![Page 37: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/37.jpg)
Future Directions
Inclusion of additional passenger-centric measures.
Application to perishable-good delivery problem (eg. just-in-time delivery).
Figure: Routes for the delivery of spare parts from CP to Drop-points for Sydney Network.
Incorporation of real-time (offline) traffic data for specific time-of-day.
Extend to include delay information.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 24/35
![Page 38: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/38.jpg)
Application to Vehicle Logistics Company: DropPoint
How to reduce distribution time from CP → DPs?
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 25/35
![Page 39: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/39.jpg)
Application to Vehicle Logistics Company: DropPoint
Sydney Network.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 26/35
![Page 40: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/40.jpg)
Application to Vehicle Logistics Company: DropPoint
Subproblem: Minimise reduced-cost, subject to:
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 27/35
![Page 41: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/41.jpg)
Application to Vehicle Logistics Company: DropPoint
Incorporate a variable link travel-time reflecting time-of-day information.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 28/35
![Page 42: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/42.jpg)
Application to Vehicle Logistics Company: DropPoint
A step-function approximation for given data granularity.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 29/35
![Page 43: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/43.jpg)
Application to Vehicle Logistics Company: DropPoint
How does our model know which time-of-day dataset to use?
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 30/35
![Page 44: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/44.jpg)
Application to Vehicle Logistics Company: DropPoint
We use a linearised model of a Heaviside step function.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 31/35
![Page 45: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/45.jpg)
Application to Vehicle Logistics Company: DropPoint
For example, if the current time is 1 : 30pm, but have discretisations of 1
hour:
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 32/35
![Page 46: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/46.jpg)
Application to Vehicle Logistics Company: DropPoint
This results in:
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 33/35
![Page 47: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/47.jpg)
Application to Vehicle Logistics Company: DropPoint
This will be used to select the correct travel-time across a link, on-the-fly.
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 34/35
![Page 48: SMART Seminar Series: Improving Public Transport Accessibility via the Optimisation and Synchronisation of Schedules for Key Transport Modes](https://reader031.vdocuments.net/reader031/viewer/2022032220/55b32a90bb61eb13228b456c/html5/thumbnails/48.jpg)
Conclusion
Thank you!
Michelle Dunbar, UoW Synchronisation ofTravel Modes within a Transport Hub 35/35