Soft Computing

, Volume 21, Issue 9, pp 2297–2306

A solid transportation model with product blending and parameters as rough variables

  • Pradip Kundu
  • Mouhya B. Kar
  • Samarjit Kar
  • Tandra Pal
  • Manoranjan Maiti
Methodologies and Application

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


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.


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

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Pradip Kundu
    • 1
  • Mouhya B. Kar
    • 2
  • Samarjit Kar
    • 3
  • Tandra Pal
    • 4
  • Manoranjan Maiti
    • 5
  1. 1.Department of Mathematics and StatisticsIISER KolkataMohanpurIndia
  2. 2.Department of Computer ScienceHeritage Institute of TechnologyKolkataIndia
  3. 3.Department of MathematicsNational Institute of Technology (NIT)DurgapurIndia
  4. 4.Department of Computer Science and EngineeringNational Institute of Technology (NIT)DurgapurIndia
  5. 5.Department of Applied MathematicsVidyasagar UniversityMidnapurIndia

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