PhD student, Industrial & Manufacturing Engineering, UW-Milwaukee

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Presentation transcript:

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

Outline Introduction Problem Description Mathematical Model Genetic Algorithm Experimental results Conclusion

Container Shipping World fleet, Feb 2004: 3167 vessels, capacity = 6.5 million 20-ft conts. (TEU) World fleet, Dec 2008: 4661 vessels, capacity = 12.1 million 20-ft conts. (TEU) World fleet, Dec 2012: 5741 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

Triple Spreader Quay Crane

Problem Description Stack Tier

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

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

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

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

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%

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.

Thank you!