1. Shabnam Lashkari Matthew Petering Yong Wu
Sequencing Triple-Spreader Crane Operations: Mathematical Formulation and Genetic Algorithm
Shabnam Lashkari
Matthew Petering
Yong Wu

2. Outline Introduction Problem Description Mathematical Model
Genetic Algorithm
Experimental results
Conclusion

3. Container Shipping

4. Container Shipping
World fleet, Feb 2004: vessels, capacity = million 20-ft conts. (TEU)
World fleet, Dec 2008: vessels, capacity = 12.1 million 20-ft conts. (TEU)
World fleet, Dec 2012: vessels, capacity = 15.4 million 20-ft conts. (TEU)
The motivation
TEU stands for Twenty-Foot Equivalent Unit which can be used to measure a ship's cargo carrying capacity

5. Problem Description
Stack 5 3 2 7 6 9 4 1 8
Tier

6. Triple Spreader Quay Crane

7. Mathematical Model Objective value:
Source:

8. Constructive heuristic
Heuristic Approach
Our overall method consists of a constructive heuristic embedded within a genetic algorithm (GA) metaheuristic.
Constructive heuristic
Stage 1
Stage 2
Build feasible crane sequences using math model.
Iteratively generate solutions, keep the bests, mutate some, cross over most.
Construct a feasible crane lift by iteratively removing containers.

9. Illustrative Instance
Handling Times:
Single lift= 1.5 min
Double lift = 1.8 min
Triple lift = 2.2 min
Changeover time = 2.7 min
Start with double spreader
Weight limits:
Dual spreader = 10
Triple spreader = 12
4 double spreader lifts
4*1.8 = 7.2 min changeover = 2.7 min
4 single spreader lifts
4*1.5 = 6 min
Changeover = 2.7 min
4 triple spreader lifts
4*2.2 = 8.8 minutes
Finished
Makespan=27.4 minutes

10. GA Setup GA was tested on 120 instances of different sizes: 3x8 5x10
Small
Medium
Large
Very large
3x8
Light
Medium
Heavy
5x10
Light
Medium
Heavy
10x23
Light
Medium
Heavy
50x50
Light
Medium
Heavy
Problem Size
3 x 8
5 x 10
10 x 23
50 x 50
Computational time limit (sec) 30
120
600

11. Results (averages) CPLEX LB 3x8L 3x8M 3x8H 5x10L 5x10M 5x10H N/A
Instance
CPLEX LB
3x8L
27.3
30.4
9.68%
26.2
4.20%
3x8M
31.7
33.8
10.83%
30.1
5.25%
3x8H
34.3
36.4
5.68%
32.0
7.13%
5x10L
53.6
51.8
57.9
10.49%
49.2
5.36%
5x10M
65.7
64.1
69.7
8.01% 59
8.64%
5x10H
71.7
70.7
73.8
9.42%
66.8
5.88%
10x23L
N/A
227.5
232.7
2.19%
205.6
10.65%
10x23M
271.6
277.9
2.23%
247.9
9.61%
10x23H
311.3
317
1.79%
294.6
5.67%
50x50L
N/A
2362.7
2398.5
1.50%
2177.6
8.50%
50x50M
2816
2837.9
0.77%
2635.1
6.86%
50x50H
3253.7
3295.8
1.28%
3098.9
4.99%

12. Conclusion
This work is a new crane scheduling problem inspired by the triple-spreader quay crane.
We formulated the problem as a mixed-integer linear program.
We developed a lower bound on the optimal value.
We devised a GA for handling large problem instances.
GA outperforms CPLEX across all problem sizes.
GA obtains solutions within 8% of optimal in most cases.

13. Thank you!