Skip to main content

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 238))

Introduction

The problems of distribution of goods from manufacturer to customer are generally described under a common heading, Transportation Problem (TP). The TP, originally developed by Hitchcock (1941), can be used when a firm tries to decide where to locate a new facility. Good financial decisions concerning facility location also attempt to minimize total transportation and production costs for the entire system. Moreover, there are many problems not exactly being called the TP but can be modelled alike.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Y.P. Aneja & K.P.K. Nair (1979), Bi-criteria Transportation Problems, Management Science 25: 73 – 78.

    Google Scholar 

  • K. Asai & H. Tanaka (1984), Fuzzy linear programming with fuzzy numbers, Fuzzy Sets and Systems 13 (1): 1 – 10.

    Google Scholar 

  • G.R. Bitran (1980), Linear multiobjective problems with interval coefficient, Management Science 26: 694 – 706.

    Google Scholar 

  • S. Chanas & D. Kuchta (1996a), A concept of solution of the Transportation Problem with fuzzy cost coefficient, Fuzzy Sets and Systems 82 (3): 299 – 305.

    Google Scholar 

  • S. Chanas & D. Kuchta (1996b), Multiobjective programming in optimization of interval objective functions – A generalized approach, European Journal of Operational Research 94 (3): 594 – 598.

    Google Scholar 

  • S. Chanas & D. Kuchta (1998), Fuzzy integer transportation problem, Fuzzy Sets and Systems 98 (3): 291 – 298. 

    Google Scholar 

  • J.W. Chinneck & K. Ramadan (2000), Linear programming with interval coefficients, Journnal of the Operational Research Society 51 (2): 209 – 220.

    Google Scholar 

  • J.N. Climaco, C.H. Antunes & M.J. Alves (1993), Interactive decision support for multiobjective transportation problems, European Journal of Operational Research 65 (1): 58 – 67.

    Google Scholar 

  • J. Current & M. Marsh (1993), Multiobjective transportation network design and routing problems: Taxonomy and annotation, European Journal of Operational Research 65 (1): 4 – 19.

    Google Scholar 

  • J. Current & H. Min (1986), Multiobjective design of transportation networks: Taxonomy and annotation, European Journal of Operational Research 26 (2): 187 – 201.

    Google Scholar 

  • S.K. Das, A. Goswami & S.S. Alam (1999), Multiobjective transportation problem with interval cost, source and destination parameters, European Journal of Operational Research 117 (1): 100 – 112.

    Google Scholar 

  • Silvio Giove (2002), Interval TOPSIS for Multicriteria Decision Making, in: M. Marinaro & R. Tagliaferri (Eds.): WIRN VIETRI 2002, Lecture Notes in Computer Science 2486, Springer-Verlag Berlin Heidelberg: 56-63.

    Google Scholar 

  • F.L. Hitchcock (1941), The distribution of a product from several sources to numerous localities, Journal of Mathematical Physics 20: 224 – 230.

    Google Scholar 

  • M. Inuiguchi & Y. Kume (1991), Goal Programming problem with Interval Coefficients and Target Intervals, European Journal of Operational Research 52 (3): 345 – 360.

    Google Scholar 

  • H. Isermann (1979), The enumeration of all efficient solutions for a Linear Multiobjective Transportation Problem, Naval Research Logistic Quarterly 26: 123 – 139; Fuzzy Sets of Systems 18 (1986): 15 – 30.

    Google Scholar 

  • H. Ishibuchi & H. Tanaka (1990), Multiobjective programming in optimization of the interval objective function, European Journal of Operational Research 48 (2): 219 –225.

    Google Scholar 

  • S. Karmakar & P.P. Mujumdar (2005), Grey Fuzzy Multiobjective Optimization Model for River Water Quality Management, Proc. of International Conference on Hydrological Perspectives for Sustainable Development (HYPESD - 2005): 923-931, IIT Roorkee, India. (Available online: http: //eprints.iisc.ernet.in /archive/ 00003153/01/Karmakar_Mujumdar_ HYPESD_2005.pdf).

    Google Scholar 

  • S. Kundu (1997), Min-transitivity of fuzzy leftness relationship and its application to decision making, Fuzzy Sets and Systems 86 (3): 357–367.

    Google Scholar 

  • S. Okada & M. Gen (1994), Order Relation between Intervals and Its Application to Shortest Path Problem, Japanese journal of Fuzzy Theory and Systems 6 (6): 703 – 717 (In English).

    Google Scholar 

  • C. Oliveira & C.H. Antunes (2007), Multiple objective linear programming models with interval coefficients – an illustrated overview, European Journal of Operational Research 181: 1434–1463.

    Google Scholar 

  • J.L. Ringuest & D.B. Rinks (1987), Interactive solutions for the Linear Multiobjective Transportation Problem, European Journal of Operations Research 32 (1): 96 – 106.

    Google Scholar 

  • A. Sengupta, T.K. Pal & D. Chakraborty (2001), Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming, Fuzzy Sets and Systems 119 (1): 129 – 138.

    Google Scholar 

  • A. Sengupta & T.K. Pal (2003), Interval-valued transportation problem with multiple penalty factors, VU Journal of Physical Sciences 9: 71 – 81.

    Google Scholar 

  • A. Sengupta & T.K. Pal (2004), Decision Maker’s Pessimistic / Optimistic Bias in an Interval-valued Transportation Problem, e-Proceedings of the First World Congress on Lateral-Computing (WCLC 2004), Bangalore, India.

    Google Scholar 

  • A.L. Soyster (1979), Inexact Linear Programming with Generalized Resource Sets, European Journal of Operational Research 3: 316-321.

    Google Scholar 

  • R.E. Steuer (1981), Algorithm for linear programming problems with interval objective function coefficient, Mathematics of Operations Research 6: 333 – 348.

    Google Scholar 

  • S. Tong (1994), Interval number and fuzzy number linear programming, Fuzzy Sets and Systems 66: 301–306.

    Google Scholar 

  • N. Yorke-Smith & C. Gervet (2001), Data uncertainty in constraint programming: a non-probabilistic approach, American Association for Artificial Intelligence 2001 Fall Symposium, November 2-4, 2001. (Available online: http: //www-users.cs.york.ac.uk/~tw/fall /Proceedings/yorke.pdf).

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sengupta, A., Pal, T.K. (2009). Interval Transportation Problem with Multiple Penalty Factors. In: Fuzzy Preference Ordering of Interval Numbers in Decision Problems. Studies in Fuzziness and Soft Computing, vol 238. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89915-0_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89915-0_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89914-3

  • Online ISBN: 978-3-540-89915-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics