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http://dx.doi.org/10.7232/iems.2012.11.2.183

Fixed Charge Transportation Problem and Its Uncertain Programming Model  

Sheng, Yuhong (College of Mathematical and System Sciences, Xinjiang University, Department of Mathematical Sciences, Tsinghua University)
Yao, Kai (Department of Mathematical Sciences, Tsinghua University)
Publication Information
Industrial Engineering and Management Systems / v.11, no.2, 2012 , pp. 183-187 More about this Journal
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;
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  • Reference
1 Balinski, M. L. (1961), Fixed-cost transportation problems, Naval Research Logistics Quarterly, 8, 41-54.   DOI
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.   DOI
3 Chanas, S., Kolodziejczyk, W., and Machaj, A. (1984), A fuzzy approach to the transportation problem, Fuzzy Sets and Systems, 13, 211-221.   DOI
4 Gao, X. (2009), Some properties of continuous uncertain measure, International Journal of Uncertain, Fuzziness and Knowledge-Based Systems, 17, 419- 426.   DOI
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.   DOI
7 Hirsch, W. M. and Dantzig, G. B. (1968), The fixed charge problem, Naval Research Logistics Quarterly, 15, 413-424.   DOI
8 Jimenez, F. and Verdegay, J. L. (1998), Uncertain solid transportation problems, Fuzzy Sets and Systems, 100, 45-57.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
21 You, C. (2009), On the convergence of uncertain sequences, Mathematical and Computer Modelling, 49, 482-487.   DOI