Fleet Management Planning

Case Study used in Ming-Che Lai, Han-Suk Sohn, Dennis L. Bricker, “A
hybrid Benders/genetic algorithm for vehicle routing and scheduling problem”
submitted for publication in International Journal of Industrial Engineering –
Theory, Applications, and Practice.

 

In this research, the hybrid Benders/genetic
algorithm was implemented to the fleet management planning of the Rockwell
Collins, Inc. headquartered in Cedar Rapids, Iowa.
We provide here some extra information for this case
study as below:

image001

 

 

Figure 1. Schematic Map of Travel Times

 

 

In this case study, travel times between the stops
were measured and shown on the schematic map in Figure 1. Now, for the purpose
of implementation, each building was labeled from 1 to 25 and the correspondences
between stop number and building are shown in Table 1. Since the travel times
between each stop can be defined to be the distances of the corresponding link,
we compute the shortest paths between every pair of nodes and record them in
the travel time matrix of a complete network (see Figure 2). These travel
times, of course, could be increased under adverse traffic and weather
conditions.

 

 

Table 1. Correspondences of
Stops and Buildings

 

Stop number

Buildings

Stop number

Buildings

Stop number

Buildings

1

126

10

109N

19

120#1

2

193

11

124N

20

171,175

3

125

12

106MR

21

Credit Union

4

Union Hall

13

168

22

137

5

127

14

153

23

139

6

191,192

15

112

24

137MR

7

133,134

16

105#1

25

138

8

118

17

120MR,121

 

 

9

109D

18

123

 

 

 

 

 

Table 2. Given Length for
Each Links

 

From      

To      

Distance

From      

To      

Distance

From      

To      

Distance

Stop 1

Stop 2

10

Stop 9

Stop 8

1

Stop 17

Stop 4

 5

Stop 1

Stop 3

10

Stop 9

Stop 10

1

Stop 17

Stop 5

 5

Stop 1

Stop 23

15

Stop 10

Stop 9

1

Stop 17

Stop 11

 4

Stop 2

Stop 1

10

Stop 10

Stop 11

1

Stop 17

Stop 12

 5

Stop 2

Stop 3

 2

Stop 11

Stop 5

3

Stop 17

Stop 16

 3

Stop 3

Stop 1

10

Stop 11

Stop 10

1

Stop 17

Stop 18

 1

Stop 3

Stop 2

 2

Stop 11

Stop 17

4

Stop 17

Stop 20

 3

Stop 3

Stop 5

 8

Stop 12

Stop 8

2

Stop 18

Stop 17

 1

Stop 3

Stop 6

 3

Stop 12

Stop 13

6

Stop 18

Stop 19

 2

Stop 3

Stop 7

 4

Stop 12

Stop 14

4

Stop 19

Stop 12

 6

Stop 3

Stop 13

 5

Stop 12

Stop 15

1

Stop 19

Stop 16

 4

Stop 4

Stop 5

 1

Stop 12

Stop 16

2

Stop 19

Stop 18

 2

Stop 4

Stop 17

 5

Stop 12

Stop 17

5

Stop 19

Stop 20

 4

Stop 5

Stop 3

 8

Stop 12

Stop 19

6

Stop 20

Stop 17

 3

Stop 5

Stop 4

 1

Stop 12

Stop 21

5

Stop 20

Stop 19

 4

Stop 5

Stop 11

 3

Stop 13

Stop 3

5

Stop 20

Stop 21

 4

Stop 5

Stop 16

 5

Stop 13

Stop 6

4

Stop 21

Stop 12

 5

Stop 5

Stop 17

 5

Stop 13

Stop 12

6

Stop 21

Stop 14

 5

Stop 6

Stop 3

 3

Stop 13

Stop 22

8

Stop 21

Stop 20

 4

Stop 6

Stop 7

 2

Stop 14

Stop 7

3

Stop 21

Stop 22

 5

Stop 6

Stop 13

 4

Stop 14

Stop 8

3

Stop 22

Stop 13

 8

Stop 7

Stop 3

 4

Stop 14

Stop 12

4

Stop 22

Stop 21

 5

Stop 7

Stop 6

 2

Stop 14

Stop 13

5

Stop 22

Stop 23

 1

Stop 7

Stop 8

 1

Stop 14

Stop 21

5

Stop 22

Stop 24

 1

Stop 7

Stop 9

 1

Stop 15

Stop 8

1

Stop 23

Stop 1

15

Stop 7

Stop 14

 3

Stop 15

Stop 12

1

Stop 23

Stop 22

 1

Stop 8

Stop 7

 1

Stop 15

Stop 16

1

Stop 23

Stop 25

 2

Stop 8

Stop 9

 1

Stop 16

Stop 5

5

Stop 24

Stop 22

 1

Stop 8

Stop 12

 2

Stop 16

Stop 12

2

Stop 24

Stop 25

 1

Stop 8

Stop 14

 3

Stop 16

Stop 15

1

Stop 25

Stop 23

 2

Stop 8

Stop 15

 1

Stop 16

Stop 17

3

Stop 25

Stop 24

 1

Stop 9

Stop 7

 1

Stop 16

Stop 19

4

 

 

 

  

image002

 

Figure 2. Shortest Path Matrix

The best solution found from
the hybrid algorithm has 137 minutes of total travel time, which consists of 48
minutes, 46 minutes, and 43 minutes for each route (see Figure 3). The travel
times, as expected, are distributed evenly among three routes in this result. Some
stops are visited each time the route is traversed, while others are visited
less frequently, according to the volume of mail and dispatches generated
there.

 

image003 

 

Figure 3. Proposed Route Plan

 

Computer programming codes
are available upon request.
Please email
to
Professor Sohn for
further enquiries regarding this case study.