Fixed Charge Transportation Problem and Its Uncertain Programming Model

- Journal title : Industrial Engineering and Management Systems
- Volume 11, Issue 2, 2012, pp.183-187
- Publisher : Korean Institute of Industrial Engineers
- DOI : 10.7232/iems.2012.11.2.183

Title & Authors

Fixed Charge Transportation Problem and Its Uncertain Programming Model

Sheng, Yuhong; Yao, Kai;

Sheng, Yuhong; Yao, Kai;

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;

Language

English

Cited by

1.

Maximal United Utility Degree Model for Fund Distributing in Higher School,;;

2.

An Individual Risk Model and Its Uncertainty Distribution,;

1.

2.

3.

4.

5.

6.

References

1.

Balinski, M. L. (1961), Fixed-cost transportation problems, Naval Research Logistics Quarterly, 8, 41-54.

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.

3.

Chanas, S., Kolodziejczyk, W., and Machaj, A. (1984), A fuzzy approach to the transportation problem, Fuzzy Sets and Systems, 13, 211-221.

4.

Gao, X. (2009), Some properties of continuous uncertain measure, International Journal of Uncertain, Fuzziness and Knowledge-Based Systems, 17, 419- 426.

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.

7.

Hirsch, W. M. and Dantzig, G. B. (1968), The fixed charge problem, Naval Research Logistics Quarterly, 15, 413-424.

8.

Jimenez, F. and Verdegay, J. L. (1998), Uncertain solid transportation problems, Fuzzy Sets and Systems, 100, 45-57.

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.

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.

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.

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.