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.

[1]  Ziyou Gao,et al.  Railway freight transportation planning with mixed uncertainty of randomness and fuzziness , 2011, Appl. Soft Comput..

[2]  P. Lingras.  Rough Neural Networks , 1996 .

[3]  Salvatore Greco,et al.  Rough sets theory for multicriteria decision analysis , 2001, Eur. J. Oper. Res..

[4]  Andrzej Skowron,et al.  Rough sets: Some extensions , 2007, Inf. Sci..

[5]  L. Polkowski.  Rough Sets: Mathematical Foundations , 2013 .

[6]  Baoding Liu,et al.  Inequalities and Convergence Concepts of Fuzzy and Rough Variables , 2003, Fuzzy Optim. Decis. Mak..

[7]  Bin Li,et al.  Rough data envelopment analysis and its application to supply chain performance evaluation , 2009 .

[8]  Lixing Yang,et al.  Fuzzy fixed charge solid transportation problem and algorithm , 2007, Appl. Soft Comput..

[9]  Z. Pawlak,et al.  Rough set approach to multi-attribute decision analysis , 1994 .

[10]  Shusaku Tsumoto,et al.  Medical Differential Diagnosis from the Viewpoint of Rough Sets , 2007 .

[11]  Ian Witten,et al.  Data Mining , 2000 .

[12]  Lixing Yang,et al.  A bicriteria solid transportation problem with fixed charge under stochastic environment , 2007 .

[13]  Salvatore Greco,et al.  Rough set approach to multiple criteria classification with imprecise evaluations and assignments , 2009, Eur. J. Oper. Res..

[14]  William Zhu,et al.  Relationship between generalized rough sets based on binary relation and covering , 2009, Inf. Sci..

[15]  Shu Xiao,et al.  A rough programming approach to power-aware VLIW instruction scheduling for digital signal processors , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[16]  Karl Rihaczek,et al.  1. WHAT IS DATA MINING? , 2019, Data Mining for the Social Sciences.

[17]  Shusaku Tsumoto,et al.  Rough representation of a region of interest in medical images , 2005, Int. J. Approx. Reason..

[18]  Jiuping Xu,et al.  A Class of Two-Person Zero-Sum Matrix Games with Rough Payoffs , 2010, Int. J. Math. Math. Sci..

[19]  Baoding Liu,et al.  Theory and Practice of Uncertain Programming , 2003, Studies in Fuzziness and Soft Computing.

[20]  Jiuping Xu,et al.  A class of rough multiple objective programming and its application to solid transportation problem , 2012, Inf. Sci..

[21]  Fernando Jiménez,et al.  Uncertain solid transportation problems , 1998, Fuzzy Sets Syst..

[22]  Ebrahim A. Youness,et al.  Characterizing solutions of rough programming problems , 2006, Eur. J. Oper. Res..

[23]  Shiang-Tai Liu,et al.  Fuzzy total transportation cost measures for fuzzy solid transportation problem , 2006, Appl. Math. Comput..

[24]  William Zhu,et al.  The algebraic structures of generalized rough set theory , 2008, Inf. Sci..

[25]  Anupam Ojha,et al.  A stochastic discounted multi-objective solid transportation problem for breakable items using Analytical Hierarchy Process , 2010 .

[26]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[27]  M. Shafiee.  Supply Chain Performance Evaluation With Rough Data Envelopment Analysis , 2022 .

[28]  Janusz Zalewski,et al.  Rough sets: Theoretical aspects of reasoning about data , 1996 .