DOI QR코드

DOI QR Code

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

  • Published : 2004.03.01

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

References

  1. Appelgren, L. H., (1969) 'A Column Generation algorithm for a ship scheduling problem', Transportation Science, 3, pp. 53-68 https://doi.org/10.1287/trsc.3.1.53
  2. Appelgren, L. H., (1971) 'Integer prograrrurung methods for a vessel scheduling problem', Transportation Science, 5, pp. 64-78 https://doi.org/10.1287/trsc.5.1.64
  3. Balas, E. and M. W. Padberg, (1976) 'Set partitioning: A survey', SIAM Review, Vol 18, No.4, pp. 710-760, Oct https://doi.org/10.1137/1018115
  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 https://doi.org/10.1002/nav.3800150305
  5. Bellmore, M., G. Bennington and S. Lubore, (1971) 'A multi-vehicle tanker scheduling problem', Transportation Science, 5, pp. 36-47 https://doi.org/10.1287/trsc.5.1.36
  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 https://doi.org/10.1287/mnsc.33.3.335
  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 https://doi.org/10.1002/nav.3800010309
  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 https://doi.org/10.1002/1520-6750(198902)36:1<27::AID-NAV3220360103>3.0.CO;2-0
  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 https://doi.org/10.1016/0305-0548(94)90083-3
  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 https://doi.org/10.1002/nav.3800130307
  14. McKay, M. D, (1974) 'Computerized scheduling of seagoing tankers', Naval Research Logistics Quarterly, 21, pp. 255-264 https://doi.org/10.1002/nav.3800210205
  15. Ronen, D, (1983) 'Cargo Ships routing and scheduling: Survey of models and problems', European Journal of Operational Research, 12, pp. 119-126 https://doi.org/10.1016/0377-2217(83)90215-1
  16. Ronen, D, (1993) 'Ship Scheduling: The Last Decade', European Journal of Operational Research, Vol. 71, pp. 325-333 https://doi.org/10.1016/0377-2217(93)90343-L
  17. Sethi, A. P. and G. L. Thompson, (1984) 'The pivot and probe algorithm for sloving a linear program', Mathmatical Programming, 29, pp. 219-233 https://doi.org/10.1007/BF02592222
  18. Whiton, J. C., (1967) 'Some constraints on shipping in linear programming models', Naval Research Logistics Quarterly, 14, pp. 257-260 https://doi.org/10.1002/nav.3800140210