Neural Computing and Applications

, Volume 31, Issue 12, pp 8593–8613 | Cite as

Multi-objective multi-item fixed-charge solid transportation problem under twofold uncertainty

  • Sankar Kumar RoyEmail author
  • Sudipta Midya
  • Gerhard-Wilhelm Weber
Original Article


In this paper, we investigate a multi-objective multi-item fixed-charge solid transportation problem (MOMIFCSTP) with fuzzy-rough variables as coefficients of the objective functions and of the constraints. The main focus of the paper is to analyze MOMIFCSTP under a fuzzy-rough environment for a transporting system. In practical situations, the parameters of a MOMIFCSTP are imprecise in nature, due to several uncontrollable factors. For these reasons, we introduce the fuzzy-rough variables in MOMIFCSTP to tackle vague data which are different from fuzziness and roughness. Fuzzy-rough expected-value operator is employed to convert fuzzy-rough MOMIFCSTP into deterministic MOMIFCSTP. Thereafter, we develop a methodology to solve the deterministic MOMIFCSTP by technique for order preference by similarity to ideal solution (TOPSIS). Three distinct approaches, namely extended TOPSIS, weighted goal programming (WGP) and fuzzy programming, are used to derive Pareto-optimal solution from the suggested model. A comparison is drawn among the optimal solutions which are derived from different approaches. It is observed from the extracted results that TOPSIS provides a better optimal solution than WGP and fuzzy programming. TOPSIS also overcomes some difficulties which arise in WGP. Finally, a real-world (industrial) problem is incorporated to show the applicability and feasibility of the proposed problem.


Fixed-charge solid transportation problem Multi-objective programming Fuzzy-rough variable Twofold uncertainty TOPSIS Fuzzy programming Weighted goal programming 


Compliance with ethical standards

Conflict of interest

The authors have no conflict of interest for the publication of this paper.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Sankar Kumar Roy
    • 1
    Email author
  • Sudipta Midya
    • 1
  • Gerhard-Wilhelm Weber
    • 2
  1. 1.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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