- AGU has bus services for personnel that have some problems, including routes not passing close to homes and long travel times. - A new clustering approach is developed to determine optimal bus stop locations. A mathematical model is formulated as a mixed integer program to find the optimal routing solution. - The new routing solution improves upon the current system by reducing the walking distance for personnel to less than 15 minutes for all, lowering the total number of stops, and increasing the number of personnel picked up while only slightly increasing the total travel distance.

1. IE 212 Deterministic Optimization
Term Project
AGU Personnel Service Buses
Route Scheduling
Kürşat Çelebi
Süleyman Daş
Şeyma Doğan
Şükrü Yasin GÜVEN

2. Abstract
• AGU has services for personnel.
• Service system has some problems.
• The new method is developed to determine
stops.
• The mathematical model is modeled as MIP.
• The new results are verified.
5/27/2016 Term Project 2

3. Current Situation
Used/Capacity Distance(km) # of Stops Departure
Time
Talas 1 25/27 16 12 07.10 am
Talas 2 18/19 13.2 12 07.20 am
Esenyurt 18/19 16 18 07.20 am
İldem 19/19 23 10 07.00 am
• Start Time : 08.00 am
• Services get by tender from private corporate
5/27/2016 Term Project 3

4. Problem
Definition
60.6
39.4
Do you use service for
transportation?
Yes
No
• 39.4% does not use
service.
5/27/2016 Term Project 4

5. Problem
Definition
17.9
39.3
39.3
3.5
Why do not you use the service?
My home is
near the
university
I prefer to use
my own car
The service is
not pass close
to my home
I lost a lot of
time in the
service
• 39.4% does not use
service.
• The service does not pass
close to my home.
• Lost a lot of time in the
service.
5/27/2016 Term Project 5

6. Problem
Definition
55.3
19.1
12.8
12.8
How long does it to walk between
stop and home?
0-5 Min
5-10 Min
10-15 Min
15+ Min
• 39.4% does not use
service.
• The service does not pass
close to my home.
• Lost a lot of time in the
service.
• 12.8% walks more than 15
min
5/27/2016 Term Project 6

7. Brief Summary
+
Current Routes
• 39.4% does not use
service.
• The service does not pass
close to my home.
• Lost a lot of time in the
service.
• 12.8% walks more than 15
min
Current Routes
Personnel Homes
5/27/2016 Term Project 7

8. Hexagonal Clustering
Approach
Main Goals
• Cover all the area
• Circumscribed circle
should be intersected as
less as possible.
• Circle
• Square
• Hexagon
• Octagon
5/27/2016 Term Project 8

9. What done?
• 39.4% does not use
service.
• The service does not pass
close to my home.
• Lost a lot of time in the
service.
• 12.8% walks more than
15 min
Suggested Stop Points
Personnel Homes
5/27/2016 Term Project 9

10. Assumptions
• All the buses capacities
are same and 27.
– Because to get equal
supply and demand
• All demands should be
satisfied.
• All demands are same
everyday.
• All demands in the
nodes are determined
by using survey results.
– Because the data that
shows who use service
and who want to use is
not given.
5/27/2016 Term Project 10

11. Mathematical
Model
Sets
i,j,p nodes
i=(AGU,2,3,…,31,32,33)
5/27/2016 Term Project 11

12. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
5/27/2016 Term Project 12

13. Mathematical
Model
Sets
I,j,p nodes i=(AGU,2,3,…,31,32,33)
veh vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Stop has 2 people
Stop has 8 people
5/27/2016 Term Project 13

14. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Distance between node 3 and 4
3
4
5/27/2016 Term Project 14

15. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Decision Variables
Mi subtour elimination variable
3
4
2
X243 the arc between node 4 and 3
Is traveled by vehicle 2
5/27/2016 Term Project 15

16. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Decision Variables
Mi subtour elimination variable
Formulations
Min z=z*=
5/27/2016 Term Project 16

17. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Decision Variables
Mi subtour elimination variable
Formulations
Min z=z*= (1)
(2)
X2AGU2+X222+X232+X242+X252+…+X2322+X2332=1
The node 2 has a node that comes before
for vehicle 2.
5/27/2016 Term Project 17

18. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Decision Variables
Mi subtour elimination variable
Formulations
Min z=z*= (1)
(2)
(3)
X2310-X21011 = 0
If 2nd vehicle goes from node 3 to 10,
It have to go from node 10 to 11
5/27/2016 Term Project 18

19. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Decision Variables
Mi subtour elimination variable
Formulations
Min z=z*= (1)
(2)
(3)
X2AGU2+X2AGU3+...+X2AGU32+X2AGU33 = 1
2nd vehicle have to leave from AGU.
(4)
5/27/2016 Term Project 19
Each vehicle leaves from AGU

20. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Decision Variables
Mi subtour elimination variable
Formulations
Min z=z*= (1)
(2)
(3)
.
(4)
(5)
Capacity constraint
5/27/2016 Term Project 20
Each vehicle leaves from AGU

21. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Decision Variables
Mi subtour elimination variable
Formulations
Min z=z*= (1)
(2)
(3)
.
(4)
(5)
(6)
MTZ(Miller-Tucker-Zemlin) formulation adds one additional
variable Mi for each city i.
MAGU – M2 +33*X2AGU2 ≤ 32
5/27/2016 Term Project 21
Each vehicle leaves from AGU

22. Mathematical
Model
Sets
i,j,p nodes i=(AGU,2,3,…,31,32,33)
veh,k vehicles veh=(1,2,3,4)
Parameters
Uveh seat capacity of vehicle veh
DELi quantity to deliver node i
Dij distance between node i and j
Decision Variables
Mi subtour elimination variable
Formulations
Min z=z*= (1)
(2)
(3)
.
(4)
(5)
(6)
(7)
5/27/2016 22
Each vehicle leaves from AGU

23. Comparison
Current System Optimal System
Total Distance 70.4 km 98.9
# of Picked Person 80 108
Walking Distance Per
Person
12.8% > 15 min All < 15 min
# of Total Stops 41 33
5/27/2016 Term Project 23

24. New Routes
5/27/2016 Term Project 24

25. The hardest part of the project
5/27/2016 Term Project 25

26. THANKS FOR LISTENING.
5/27/2016 Term Project 26