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A study on the column subtraction method applied to ship scheduling problem
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 Title & Authors
A study on the column subtraction method applied to ship scheduling problem
Hwang, Hee-Su; Lee, Hee-Yong; Kim, Si-Hwa;
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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.
Column Subtraction;Ship Scheduling Problem;Set Packing;Set Partitioning;Set Covering;Branch-and-Bound;
 Cited by
항만의 비선형 지체 비용을 고려한 선박의 우회 경로 결정 문제에 관한 연구,양병학;

대한설비관리학회지, 2016. vol.21. 2, pp.31-41
Appelgren, L. H., (1969) 'A Column Generation algorithm for a ship scheduling problem', Transportation Science, 3, pp. 53-68 crossref(new window)

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

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

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

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

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 crossref(new window)

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 crossref(new window)

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 crossref(new window)

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

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 crossref(new window)

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

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

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 crossref(new window)

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

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

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

Sethi, A. P. and G. L. Thompson, (1984) 'The pivot and probe algorithm for sloving a linear program', Mathmatical Programming, 29, pp. 219-233 crossref(new window)

Whiton, J. C., (1967) 'Some constraints on shipping in linear programming models', Naval Research Logistics Quarterly, 14, pp. 257-260 crossref(new window)