A study on the column subtraction method applied to ship scheduling problem

- Journal title : Journal of Navigation and Port Research
- Volume 28, Issue 2, 2004, pp.129-133
- Publisher : Korean Institute of Navigation and Port Research
- DOI : 10.5394/KINPR.2004.28.2.129

Title & Authors

A study on the column subtraction method applied to ship scheduling problem

Hwang, Hee-Su; Lee, Hee-Yong; Kim, Si-Hwa;

Hwang, Hee-Su; Lee, Hee-Yong; Kim, Si-Hwa;

Abstract

Column subtraction, originally proposed by Harche and Thompson(1994), is an exact method for solving large set covering, packing and partitioning problems. Since the constraint set of ship scheduling problem(SSP) have a special structure, most instances of SSP can be solved by LP relaxation This paper aim, at applying the column subtraction method to solve SSP which am not be solved by LP relaxation For remained instances of unsolvable ones, we subtract columns from the finale simplex table to get another integer solution in an iterative manner. Computational results having up to 10,000 0-1 variables show better performance of the column subtraction method solving the remained instances of SSP than complex branch and-bound algorithm by LINDO.

Keywords

Column Subtraction;Ship Scheduling Problem;Set Packing;Set Partitioning;Set Covering;Branch-and-Bound;

Language

English

Cited by

1.

항만의 비선형 지체 비용을 고려한 선박의 우회 경로 결정 문제에 관한 연구,양병학;

대한설비관리학회지, 2016. vol.21. 2, pp.31-41

References

1.

Appelgren, L. H., (1969) 'A Column Generation algorithm for a ship scheduling problem', Transportation Science, 3, pp. 53-68

2.

Appelgren, L. H., (1971) 'Integer prograrrurung methods for a vessel scheduling problem', Transportation Science, 5, pp. 64-78

3.

Balas, E. and M. W. Padberg, (1976) 'Set partitioning: A survey', SIAM Review, Vol 18, No.4, pp. 710-760, Oct

4.

Bellmore, M., (1968) 'A maximum utility solution to a vehicle constrained tanker scheduling problem', Naval Research Logistics Quarterly, 15, No.3, pp. 403-411

5.

Bellmore, M., G. Bennington and S. Lubore, (1971) 'A multi-vehicle tanker scheduling problem', Transportation Science, 5, pp. 36-47

6.

Brown, G. G., G. W. Graves and D. Ronen, (1987) 'Scheduling ocean transportation of crude oil', Management Science, Vo. 33, No.3, pp. 335-346

7.

Dantzig, G. B. and D. R. Fulkerson, (1954) 'Minimizing the nwnber of tankers to meet a fixed schedule', Naval Research Logistics Quarterly, Vol. 1, pp. 217-222

8.

Fisher, M. L. and M. B. Rosenwein, (1989) 'An interactive optimization system for bulk-cargo Ship Scheduling', Naval Research Logistics, Vol. 36, pp. 27-42

9.

George L. Nemhauser, Laurence A. Wolsey, 1988 , Integer and Combinatorial Optimization, Wiley

10.

Harche, F. and G. L. Thompson, (1994) 'The column subtraction Algorithm: An exact method for solving weighted set covering, packing and partitioning problems', Computers & Operations Research, Vol. 21, No.6, pp. 689-705

11.

Kim, Si-Hwa and Kyung-Keun Lee, (1997) 'An Optimization-based decision support system for ship scheduling', Computers & I.E., An IntI. Journal, Vol. 33, pp. 689-692

12.

Kim, Si-Hwa, (1999) 'Optimization-based Decision Support System for Some Maritime. Transportation Problems', Ph D. Thesis, Dept. of Industrial Engineering, Pusan National University

13.

Laderman, J. and L. Gleiberman, J. F. Egan, (1966) Vessel Allocation By Linear Programming', Naval Research Logistics Quarterly, Vol. 13, No.3, pp. 315-320, Sep

14.

McKay, M. D, (1974) 'Computerized scheduling of seagoing tankers', Naval Research Logistics Quarterly, 21, pp. 255-264

15.

Ronen, D, (1983) 'Cargo Ships routing and scheduling: Survey of models and problems', European Journal of Operational Research, 12, pp. 119-126

16.

Ronen, D, (1993) 'Ship Scheduling: The Last Decade', European Journal of Operational Research, Vol. 71, pp. 325-333