Skip to main content
SpringerLink
Log in

Fixed Charge Bulk Transportation Problem

  • Conference paper
  • First Online:
Operations Research and Optimization (FOTA 2016)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 225))

Abstract

This paper discusses an exact method to solve fixed charge bulk transportation problem (FCBTP). The fixed charge bulk transportation problem is a variant of the classical transportation problem in which a fixed cost is incurred in addition to the bulk transportation cost. This paper comprises of two sections. In Sect. 2, an algorithm based on lexi-search approach is proposed to solve FCBTP which gives the optimal solution in a finite number of iterations. Section 3 reports and corrects the errors which occurred in the paper entitled ‘Solving the fixed charge problem by ranking the extreme point’ by Murty (Oper. Res. 16(2): 268–279, 1968) [24]. Towards the end, some Concluding Remarks are given.

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

Access this chapter

Log in via an institution
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 EPUB and 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

References

  1. Adlakha, V., Kowalski, K.: On the fixed-charge transportation problem. Omega 27(27), 381–388 (1999)

    Article  Google Scholar 

  2. Adlakha, V., Kowalski, K.: A simple heuristic for solving small fixed-charge transportation problems. Omega 31(3), 205–211 (2003)

    Article  Google Scholar 

  3. Adlakha, V., Kowalski, K., Vemuganti, R.R., Lev, B.: More-for-less algorithm for fixed charge transportation problems. OMEGA Int. J. Manag. Sci. 35(1), 116–127 (2007)

    Article  Google Scholar 

  4. Adlakha, V., Kowalski, K., Wang, S., Lev, B., Shen, W.: On approximation of the fixed charge transportation problem. Omega 43, 64–70 (2014)

    Article  Google Scholar 

  5. Aguado, J.: Fixed charge transportation problems: a new heuristic approach based on lagrangean relaxation and the solving of core problems. Ann. Oper. Res. 172, 45–69 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Arora, S.R., Ahuja, A.: A Paradox in a fixed charge transportation problem. Indian J. Pure Appl. Math. 31(7), 809–822 (2000)

    Google Scholar 

  7. Arora, S., Puri, M.C.: A variant of time minimizing assignment problem. Eur. J. Oper. Res. 110, 314–325 (1998)

    Article  MATH  Google Scholar 

  8. Balas, E., Glover, F., Zionts, S.: An additive algorithm for solving linear programs with zero one variables. Oper. Res. INFORMS 13(4), 517–549 (1965)

    Article  MathSciNet  Google Scholar 

  9. Balinski, M.L.: Fixed-cost transportation problems. Nav. Res. Logist. Q. 8(01), 41–54 (1961)

    Article  MATH  Google Scholar 

  10. Caramia, M., Guerreio, F.: A heuristic approach to long-haul freight transportation with multiple objective functions. OMEGA Int. J. Manag. Sci. 37, 600–614 (2009)

    Article  Google Scholar 

  11. Cooper, L., Drebes, C.: An approximate solution method for the fixed charge problem. Nav. Res. Logist. Q. 14(1) (1967)

    Google Scholar 

  12. Cooper, L.: The fixed charge problem-I: a new heuristic method. Comput. Math. Appl. 1(1), 89–95 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cooper, L., Olson, A.M.: Random Perturbations and MI-MII Heuristics for the Fixed Charge Problem

    Google Scholar 

  14. De Maio, A., Roveda, C.: An all zero-one algorithm for a certain class of transportation problems. INFORMS 19(6), 1406–1418 (1969)

    MATH  Google Scholar 

  15. Denzler, D.R.: An approximative algorithm for the fixed charge problem. Nav. Res. Logist. Q. 16(3) (1969)

    Google Scholar 

  16. Gray, P.: Exact solution of the fixed-charge transportation problem. Oper. Res. 19(6), 1529–1538 (1971)

    Article  MATH  Google Scholar 

  17. Hajiaghaei-Keshteli, M., Molla-Alizadeh-Zavardehi, S., Tavakkoli-Moghaddam, R.: Addressing a non linear fixed-charge transportation using a spanning tree based genetic algorithm. Comput. Ind. Eng. 59, 259–271 (2010)

    Article  Google Scholar 

  18. Jo, J., Li, Y., Gen, M.: Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Comput. Ind. Eng. 53, 290–298 (2007)

    Article  Google Scholar 

  19. Kowalski, K., Lev, B.: On step fixed-charge transportation problem. OMEGA Int. J. Manag. Sci. 36(5), 913–917 (2008)

    Article  Google Scholar 

  20. Kowalski, K., Lev, B., Shen, W., Tu, Y.: A fast and simple branching algorithm for solving small scale fixed-charge transportation problem. Oper. Res. Perspect. 1(1), 1–5 (2014)

    Article  MathSciNet  Google Scholar 

  21. Liu, S.-T.: The total cost bounds of transportation problem with varying demand and supply. OMEGA Int. J. Manag. Sci. 31(4), 247–251 (2003)

    Article  Google Scholar 

  22. Ma, H., Miao, Z., Lim, A., Rodrigues, B.: Cross docking distribution networks with setup cost and time window constraint. OMEGA Int. J. Manag. Sci. 39(1), 64–72 (2011)

    Article  Google Scholar 

  23. Murthy, M.S.: A bulk transportation problem. OPSEARCH 13(3–4), 143–155 (1976)

    MathSciNet  Google Scholar 

  24. Murty, K.G.: Solving the fixed charge problem by ranking the extreme points. Oper. Res. 16(2), 268–279 (1968)

    Article  MATH  Google Scholar 

  25. Ortega, F., Wolsey, L.: A branch and cut algorithm for the single-commodity, uncapacitated, fixed charge network flow problem. Networks 41, 143–158 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  26. Puri, M.C., Swarup, K.: A systematic extreme point enumeration procedure for fixed charge problem. Trab Estad y Investig Oper. 25(1), 99–108 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  27. Robers, P., Cooper, L.: A study of the fixed charge transportation problem. Comput. Math. Appl. 2(2), 125–135 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sadagopan, S., Ravindran, A.: A vertex ranking algorithm for the fixed-charge transportation problem. J. Optim. Theory Appl. 37(2) (1982)

    Google Scholar 

  29. Srinivasan, V., Thompson, G.L.: An algorithm for assigning uses to sources in a special class of transportation problems. INFORMS 21(1), 284–295 (1973)

    MATH  Google Scholar 

  30. Steinberg, D.I.: The fixed charge problem. Nav. Res. Logist. Q. 17(2) (1970)

    Google Scholar 

  31. Thirwani, D.: A note on fixed charge Bi-Criterion transportation problem with enhanced flow. Indian J. Pure Appl. Math. 29(5), 565–571 (1998)

    Google Scholar 

  32. Walker, W.: A heuristic adjacent extreme point algorithm for fixed charge problem. Manag. Sci. 22, 587–596 (1976)

    Article  MATH  Google Scholar 

  33. Warren, M.H, George, B.D.: The fixed charge problem. RAND Corp. RM-1383, 413–424 (1954)

    Google Scholar 

  34. Warren, M.H., Hoffman, A.J.: Extreme varieties, concave functions, and the fixed charge problem. Commun. Pure Appl. Math. XIV, 355–369(1961)

    Google Scholar 

Download references

Acknowledgements

The authors are thankful to the honourable reviewers for their significant comments which have enhanced the quality of our manuscript ‘Fixed Charge Bulk Transportation Problem’ to a great extent.

Author information

Authors and Affiliations

  1. Indira Gandhi Delhi Technical University For Women, Kashmere Gate, New Delhi, 110006, India

    Bindu Kaushal & Shalini Arora

Authors
  1. Bindu Kaushal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shalini Arora
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bindu Kaushal .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Durgapur, Durgapur, West Bengal, India

    Samarjit Kar

  2. Department of Computer Science and Engineering, Jadavpur University, Kolkata, West Bengal, India

    Ujjwal Maulik

  3. School of Economics and Management, Beijing University of Chemical Technology, Beijing, China

    Xiang Li

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kaushal, B., Arora, S. (2018). Fixed Charge Bulk Transportation Problem. In: Kar, S., Maulik, U., Li, X. (eds) Operations Research and Optimization. FOTA 2016. Springer Proceedings in Mathematics & Statistics, vol 225. Springer, Singapore. https://doi.org/10.1007/978-981-10-7814-9_22

Download citation

Publish with us

Policies and ethics

Search

Navigation