A solid transportation model with product blending and parameters as rough variables Pradip Kundu Mouhya B. Kar Samarjit Kar Email author Tandra Pal Manoranjan Maiti Methodologies and Application First Online: 23 November 2015 DOI :
10.1007/s00500-015-1941-9

Cite this article as: Kundu, P., Kar, M.B., Kar, S. et al. Soft Comput (2017) 21: 2297. doi:10.1007/s00500-015-1941-9
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Abstract In this paper, we formulate a practical solid transportation problem with product blending which is a common issue in many operational and planning models in the chemical, petroleum, gasoline and process industries. In the problem formulation, we consider that raw materials from different sources with different quality (or purity) levels are to be transported to some destinations so that the materials received at each destination can be blended together into the final product to meet minimum quality requirement of that destination. The parameters such as transportation costs, availabilities, demands are considered as rough variables in designing the model. We construct a rough chance-constrained programming (RCCP) model for the problem with rough parameters based on trust measure. This RCCP model is then transformed into deterministic form to solve the problem. Numerical example is presented to illustrate the problem model and solution strategy. The results are obtained using the standard optimization solver LINGO.

Keywords Solid transportation problem Blending Rough variable Trust measure Chance-constrained programming

References Chanas S, Kuchta D (1996) A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets Syst 82:299–305

MathSciNet CrossRef Google Scholar DeWitt C, Lasdon L, Waren A, Brenner D, Melhem S (1989) OMEGA—an improved gasoline blending system for Texaco. Interfaces 19(1):85–101

CrossRef Google Scholar Haley KB (1962) The sold transportation problem. Oper Res 10:448–463

CrossRef MATH Google Scholar Hitchcoockk FL (1941) The distribution of product from several sources to numerous localities. J Math Phys 20:224–230

MathSciNet CrossRef Google Scholar Jiménez F, Verdegay JL (1998) Uncertain solid transportation problems. Fuzzy Sets Syst 100:45–57

MathSciNet CrossRef Google Scholar Jiménez F, Verdegay JL (1999) Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach. Eur J Oper Res 117:485–510

CrossRef MATH Google Scholar Kaur A, Kumar A (2012) A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers. Appl Soft Comput 12(3):1201–1213

CrossRef Google Scholar Kelly JD, Mann JL (2003) Crude oil blend scheduling optimization: an application with multimillion dollar benefits. Hydrocarb Process 82(6):47–53

Google Scholar Kundu P, Kar S, Maiti M (2013a) Multi-objective multi-item solid transportation problem in fuzzy environment. Appl Math Model 37:2028–2038

MathSciNet CrossRef MATH Google Scholar Kundu P, Kar S, Maiti M (2013b) Some solid transportation models with crisp and rough costs. Int J Math Comput Phys Electr Comput Eng 73:185–192

Kundu P, Kar S, Maiti M (2014) Multi-objective solid transportation problems with budget constraint in uncertain environment. Int J Syst Sci 45(8):1668–1682

MathSciNet CrossRef MATH Google Scholar Liu B (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg

CrossRef MATH Google Scholar Liu B (2003) Inequalities and convergence concepts of fuzzy and rough variables. Fuzzy Opt Decis Mak 2:87–100

MathSciNet CrossRef Google Scholar Liu B (2004) Uncertainty theory: an introduction to its axiomatic foundations. Springer, Berlin

CrossRef MATH Google Scholar Liu B, Iwamura K (1998) Chance constrained programming with fuzzy parameters. Fuzzy Sets Syst 94(2):227–237

MathSciNet CrossRef MATH Google Scholar Liu L, Zhu Y (2007) Rough variables with values in measurable spaces. Inf Sci 177:4678–4685

MathSciNet CrossRef MATH Google Scholar Liu S (2006) Fuzzy total transportation cost measures for fuzzy solid transportation problem. Appl Math Comput 174:927–941

MathSciNet MATH Google Scholar Méndez CA, Grossmann IE, Harjunkoski I, Kaboré P (2006) A simultaneous optimization approach for off-line blending and scheduling of oil-refinery operations. Comput Chem Eng 30:614–634

CrossRef Google Scholar Misener R, Floudas CA (2009) Advances for the pooling problem: modeling, global optimization, and computational studies survey. Appl Comput Math 8(1):3–22

MathSciNet MATH Google Scholar Mondal M, Maity AK, Maiti MK, Maiti M (2013) A production-repairing inventory model with fuzzy rough coefficients under inflation and time value of money. Appl Math Model 37:3200–3215

MathSciNet CrossRef MATH Google Scholar Nagarjan A, Jeyaraman K (2010) Solution of chance constrained programming problem for multi-objective interval solid transportation problem under stochastic environment using fuzzy approach. Int J Comput Appl 10(9):19–29

Google Scholar Ojha A, Das B, Mondal S, Maity M (2009) An entropy based solid transportation problem for general fuzzy costs and time with fuzzy equality. Math Comput Model 50(1–2):166–178

MathSciNet CrossRef MATH Google Scholar Papageorgiou DJ, Toriello A, Nemhauser GL, Savelsbergh MWP (2012) Fixed-charge transportation with product blending. Transp Sci 46(2):281–295

CrossRef Google Scholar Pawlak Z (1982) Rough sets. Int J Inf Comput Sci 11(5):341–356

CrossRef MATH Google Scholar Pawlak Z (1991) Rough sets—theoretical aspects of reasoning about data. Kluwer Academatic Publishers, Boston

MATH Google Scholar Pawlak Z, Skowron A (2007) Rough sets: some extensions. Inf Sci 177:28–40

MathSciNet CrossRef MATH Google Scholar Polkowski L (2002) Rough sets, mathematical foundations. Physica-Verlag, Heidelberg

Rigby B, Lasdon L, Waren A (1995) The evolution of Texaco’s blending systems: from OMEGA to StarBlend. Interfaces 25(5):64–83

CrossRef Google Scholar Romo F, Tomasgar A, Hellemo L, Fodstad M, Eidesen BH, Pedersen B (2009) Optimizing the Norwegian natural gas production and transport. Interfaces 39(1):46–56

CrossRef Google Scholar Tao Z, Xu J (2012) A class of rough multiple objective programming and its application to solid transportation problem. Inf Sci 188:215–235

MathSciNet CrossRef MATH Google Scholar Xu J, Yao L (2010) A class of two-person zero-sum matrix games with rough payoffs. Int J Math Math Sci. doi:

10.1155/2010/404792
MathSciNet MATH Google Scholar Xu J, Li B, Wu D (2009) Rough data envelopment analysis and its application to supply chain performance evaluation. Int J Prod Econ 122:628–638

CrossRef Google Scholar Yang L, Feng Y (2007) A bicriteria solid transportation problem with fixed charge under stochastic environment. Appl Math Model 31:2668–2683

CrossRef MATH Google Scholar Yang L, Liu L (2007) Fuzzy fixed charge solid transportation problem and algorithm. Appl Soft Comput 7:879–889

CrossRef Google Scholar Youness E (2006) Characterizing solutions of rough programming problems. Eur J Oper Res 168:1019–1029

MathSciNet CrossRef MATH Google Scholar © Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations Pradip Kundu Mouhya B. Kar Samarjit Kar Email author Tandra Pal Manoranjan Maiti 1. Department of Mathematics and Statistics IISER Kolkata Mohanpur India 2. Department of Computer Science Heritage Institute of Technology Kolkata India 3. Department of Mathematics National Institute of Technology (NIT) Durgapur India 4. Department of Computer Science and Engineering National Institute of Technology (NIT) Durgapur India 5. Department of Applied Mathematics Vidyasagar University Midnapur India