1. PhD student, Industrial & Manufacturing Engineering, UW-Milwaukee
Sequencing Triple Spreader Crane Operations: Mathematical Formulation and Genetic Algorithm
Shabnam Lashkari
PhD student, Industrial & Manufacturing Engineering, UW-Milwaukee
Matthew Petering
Associate Professor, Industrial & Manufacturing Engineering, UW-Milwaukee
Yong Wu
Senior Lecturer, Griffith Business School, Griffith University, Australia

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

3. 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

4. Triple Spreader Quay Crane

5. Problem Description
Stack
Tier

6. 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

7. Mathematical Model Weight limits: Dual spreader = 10
Triple spreader = 12
Deriving L2st, L3st
Objective value:

8. Genetic Algorithm Tier 3 Options (Categorized & Ranked)
At least 1 double & 1 triple
1 (S, T, T, T, D, D, D, D) Objective = 7.3 .
At least 1 double & no triples
16 (S, D, D, D, D, D, D, S) Objective = 8.4
At least 1 triple & no doubles
37 (S, S, T, T, T, T, T, T) Objective = 7.4
No doubles and no triples
44 (S, S, S, S, S, S, S, S) Objective = 12
Tier 2 Options
At least 1 double & 1 triple
At least 1 double & no triples
At least 1 triple & no doubles
No doubles and no triples 12
Tier 1 Options
At least 1 double & 1 triple
At least 1 double & no triples
At least 1 triple & no doubles
No doubles and no triples 12

9. 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

10. 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%

11. 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.

12. Thank you!