DOI QR코드

DOI QR Code

Fixed Charge Transportation Problem and Its Uncertain Programming Model

  • Sheng, Yuhong ;
  • Yao, Kai
  • Received : 2012.02.14
  • Accepted : 2012.04.23
  • Published : 2012.06.30

Abstract

In this paper, we study the fixed charge transportation problem with uncertain variables. The fixed charge transportation problem has two kinds of costs: direct cost and fixed charge. The direct cost is the cost associated with each source-destination pair, and the fixed charge occurs when the transportation activity takes place in the corresponding source-destination pair. The uncertain fixed charge transportation problem is modeled on the basis of uncertainty theory. According to inverse uncertainty distribution, the model can be transformed into a deterministic form. Finally, in order to solve the uncertain fixed charge transportation problem, a numerical example is given to show the application of the model and algorithm.

Keywords

Transportation Problem;Uncertainty Theory;Uncertain Variable;Uncertain Measure;Uncertain Programming

References

  1. Balinski, M. L. (1961), Fixed-cost transportation problems, Naval Research Logistics Quarterly, 8, 41-54. https://doi.org/10.1002/nav.3800080104
  2. Bit, A. K., Biswal, M. P., and Alam, S. S. (1993), Fuzzy programming approach to multiobjective solid transportation problem, Fuzzy Sets and Systems, 57, 183-194. https://doi.org/10.1016/0165-0114(93)90158-E
  3. Chanas, S., Kolodziejczyk, W., and Machaj, A. (1984), A fuzzy approach to the transportation problem, Fuzzy Sets and Systems, 13, 211-221. https://doi.org/10.1016/0165-0114(84)90057-5
  4. Gao, X. (2009), Some properties of continuous uncertain measure, International Journal of Uncertain, Fuzziness and Knowledge-Based Systems, 17, 419- 426. https://doi.org/10.1142/S0218488509005954
  5. Gottlieb, J. and Paulmann, L. (1998), Genetic algorithms for the fixed charge transportation problem, Proceedings of the IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, 330-335.
  6. Haley, K. B. (1962), New methods in mathematical programming: the solid transportation problem, Operations Research, 10, 448-463. https://doi.org/10.1287/opre.10.4.448
  7. Hirsch, W. M. and Dantzig, G. B. (1968), The fixed charge problem, Naval Research Logistics Quarterly, 15, 413-424. https://doi.org/10.1002/nav.3800150306
  8. Jimenez, F. and Verdegay, J. L. (1998), Uncertain solid transportation problems, Fuzzy Sets and Systems, 100, 45-57. https://doi.org/10.1016/S0165-0114(97)00164-4
  9. Jimenez, F. and Verdegay, J. L. (1999), Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach, European Journal of Operational Research, 117, 485-510. https://doi.org/10.1016/S0377-2217(98)00083-6
  10. Klingman, D., Napier, A., and Stutz, J. (1974), NETGEN: a program for generating large scale capacitated assignment, transportation, and minimum cost flow network problems, Management Science, 20, 814-821. https://doi.org/10.1287/mnsc.20.5.814
  11. Li, X. and Liu, B. (2009), Hybrid logic and uncertain logic, Journal of Uncertain Systems, 2, 83-94.
  12. Li, Y., Ida, K., Gen, M., and Kobuchi, R. (1997), Neural network approach for multicriteria solid transportation problem, Computers and Industrial Engineering, 33, 465-468. https://doi.org/10.1016/S0360-8352(97)00169-1
  13. Liu, B. (2007), Uncertainty Theory (2nd ed.), Springer- Verlag, Berlin, Germany.
  14. Liu, B. (2009a), Some research problems in uncertainty theory, Journal of Uncertain Systems, 3, 3-10.
  15. Liu, B. (2009b), Theory and Practice of Uncertain Programming (2nd ed.), Springer-Verlag, Berlin, Germany.
  16. Liu, B. (2010a), Uncertain set theory and uncertain inference rule with application to uncertain control, Journal of Uncertain Systems, 4, 83-98.
  17. Liu, B. (2010b), Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, Springer, Heidelberg, Germany.
  18. Liu, B. (2008), Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems, 2, 3-16.
  19. Srinivasan, V. and Thompson, G. L. (1972), An operator theory of parametric programming for the transportation problem-II, Naval Research Logistics Quarterly, 19, 227-252. https://doi.org/10.1002/nav.3800190203
  20. Sun, M., Aronson, J. E., McKeown, P. G., and Drinka, D. (1998), A tabu search heuristic procedure for the fixed charge transportation problem, European Journal of Operational Research, 106, 441-456. https://doi.org/10.1016/S0377-2217(97)00284-1
  21. You, C. (2009), On the convergence of uncertain sequences, Mathematical and Computer Modelling, 49, 482-487. https://doi.org/10.1016/j.mcm.2008.07.007

Cited by

  1. Maximal United Utility Degree Model for Fund Distributing in Higher School vol.12, pp.1, 2013, https://doi.org/10.7232/iems.2013.12.1.036
  2. An Individual Risk Model and Its Uncertainty Distribution vol.12, pp.1, 2013, https://doi.org/10.7232/iems.2013.12.1.046
  3. Two Uncertain Programming Models for Inverse Minimum Spanning Tree Problem vol.12, pp.1, 2013, https://doi.org/10.7232/iems.2013.12.1.009
  4. Emergency Rescue Location Model with Uncertain Rescue Time vol.2014, pp.1563-5147, 2014, https://doi.org/10.1155/2014/464259
  5. An Uncertain Programming for the Integrated Planning of Production and Transportation vol.2014, pp.1563-5147, 2014, https://doi.org/10.1155/2014/419358
  6. Dispatching medical supplies in emergency events via uncertain programming vol.28, pp.3, 2017, https://doi.org/10.1007/s10845-014-1008-2
  7. Uncertain programming models for fixed charge multi-item solid transportation problem pp.1433-7479, 2017, https://doi.org/10.1007/s00500-017-2718-0
  8. Two empirical uncertain models for project scheduling problem vol.66, pp.9, 2015, https://doi.org/10.1057/jors.2014.115
  9. Multi-Objective Fixed-Charge Transportation Problem with Random Rough Variables vol.26, pp.06, 2018, https://doi.org/10.1142/S0218488518500435
  10. Optimizing Movement of Students from Hostels to Lecture Rooms in a Potential World Class University Using Transportation Model vol.09, pp.06, 2018, https://doi.org/10.4236/am.2018.96044