Some Solid Transportation Models with Crisp and Rough Costs
In this paper, some practical solid transportation models are formulated considering per trip capacity of each type of conveyances with crisp and rough unit transportation costs. This is applicable for the system in which full vehicles, e.g. trucks, rail coaches are to be booked for transportation of products so that transportation cost is determined on the full of the conveyances. The models with unit transportation costs as rough variables are transformed into deterministic forms using rough chance constrained programming with the help of trust measure. Numerical examples are provided to illustrate the proposed models in crisp environment as well as with unit transportation costs as rough variables.
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 K. Dembczynski, S. Greco, R. Slowinski, Rough set approach to multiple criteria classification with imprecise evaluations and assignments, European Journal of Operational Research 198 (2009) 626-636.
 S. Greco, B. Matarazzo, R. Slowinski, Rough sets theory for multicriteria decision analysis, European Journal of Operational Research 129 (2001) 1-47.
 K.B.Haley, The sold transportation problem, Operations Research 10 (1962) 448-463.
 S. Hirano, S. Tsumoto, Rough representation of a region of interest in medical images, International Journal of Approximate Reasoning 40 (2005) 23-34.
 F.Jim'enez, J.L.Verdegay, Uncertain solid transportation problems, Fuzzy Sets and Systems, 100 (1998) 45-57.
 T. Lin, Y. Yao, L. Zadeh, Data Mining, Rough Sets, and Granular Computing, Springer Verlag, 2002.
 P. Lingras, Rough Neural Networks, International Conference on Information Processing and Management of Uncertainty, Granada, Spain, 1996, 1445-1450.
 B. Liu, Theory and Practice of Uncertain Programming, Physical-Verlag, Heidelberg, 2002.
 B. Liu, Uncertainty Theory: An Introduction to its Axiomatic Foundation, Springer-Verlag, Berlin, 2004.
 B. Liu, Inequalities and Convergence Concepts of Fuzzy and Rough Variables, Fuzzy Optimization and Decision Making 2 (2003) 87-100.
 G. Liu, W. Zhu, The algebraic structures of generalized rough set theory, Information Sciences 178 (2008) 4105-4113.
 S. Liu, Fuzzy total transportation cost measures for fuzzy solid transportation problem, Applied Mathematics and Computation 174 (2006) 927-941.
 A. Nagarjan, K. Jeyaraman, Solution of chance constrained programming problem for multi-objective interval solid transportation problem under stochastic environment using fuzzy approach, International Journal of Computer Applications 10(9) (2010) 19-29.
 A.Ojha, B.Das, S.Mondal, M.Maiti, An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality, Mathematical and Computer Modeling, 50 (1-2) (2009) 166-178.
 A. Ojha, B. Das, S. Mondal, M. Maiti, A stochastic discounted multiobjective solid transportation problem for breakable items using analytical hierarchy process, Applied Mathematical Modelling 34 (2010) 2256- 2271.
 Z. Pawlak, Rough sets, International Journal of Information and Computer Sciences 11(5) (1982) 341-356.
 Z. Pawlak, Rough Sets - Theoretical Aspects of Reasoning About Data, Kluwer Academatic Publishers, Boston, 1991.
 Z. Pawlak, R. Slowinski, Rough set approach to multi-attribute decision analysis (invited review), European Journal of Operational Research 72 (1994) 443-459.
 Z. Pawlak, A. Skowron, Rough sets: some extensions, Information Sciences 177 (2007) 28-40.
 L. Polkowski: Rough Sets, Mathematical Foundations, Advances in Soft Computing, Physica Verlag, A Springer-Verlag Company, 2002.
 E.D.Schell, Distribution of a product by several properties, Proceedings of 2nd Symposium in Linear Programming, DCS/comptroller, HQ US Air Force, Washington D C (1955) 615-642.
 M. Shafiee, N. Shams-e-alam, Supply Chain Performance Evaluation With Rough Data Envelopment Analysis, 2010 International Conference on Business and Economics Research, vol.1 (2011), IACSIT Press, Kuala Lumpur, Malaysia.
 Z. Tao, J. Xu, A class of rough multiple objective programming and its application to solid transportation problem, Information Sciences 188 (2012) 215235.
 S. Tsumoto, Medical differential diagnosis from the viewpoint of rough sets, Information Sciences (2007) 28-34.
 J. Xu and L. Yao, A Class of Two-Person Zero-Sum Matrix Games with Rough Payoffs, International Journal of Mathematics and Mathematical Sciences 2010, doi:10.1155/2010/404792.
 J. Xu, B. Li, D. Wu, Rough data envelopment analysis and its application to supply chain performance evaluation, International Journal of Production Economics 122 (2009) 628-638.
 Shu Xiao and Edmund M-K. Lai, A Rough programming approach to power-aware VLIW instruction scheduling for digital signal processors, ICASSP 2005.
 L. Yang, Y. Feng, A bicriteria solid transportation problem with fixed charge under stochastic environment, Applied Mathematical Modelling 31 (2007) 2668-2683.
 L. Yang, L. Liu, Fuzzy fixed charge solid transportation problem and algorithm, Applied Soft Computing 7 (2007) 879-889.
 L. Yang, Z. Gao, K. Li, Railway freight transportation planning with mixed uncertainty of randomness and fuzziness, Applied Soft Computing 11 (2011) 778-792.
 E. Youness, Characterizing solutions of rough programming problems, European Journal of Operational Research 168 (2006) 1019-1029.
 W. Zhu, Relationship between generalized rough sets based on binary relation and covering, Information Sciences 179 (2009) 210-225.