Total views : 289

OFSTF Method- An Optimal Solution for Transportation Problem

Affiliations

  • Department of Mathematics, Mother Teresa Women’s University, Kodaikanal - 624101, Tamil Nadu, India
  • Department of Mathematics, PSNA College of Engineering and Technology, Dindigul - 624622, Tamil Nadu, India

Abstract


In this paper a different approach OFSTF (Origin, First, Second, Third, and Fourth quadrants) Method is applied for finding a feasible solution for transportation problems directly. The proposed method is a unique, it gives always feasible (may be optimal for some extant) solution without disturbance of degeneracy condition. This method takes least iterations to reach optimality. A numerical example is solved to check the validity of the proposed method and degeneracy problem is also discussed.

Keywords

Assignment Problem, Degeneracy, Pay Off Matrix (POM), Quadrants, Transportation Problem.

Full Text:

 |  (PDF views: 309)

References


  • Arsham H, Kahn AB. A simplex-typealgorithm for general transportation problems: An alternative to Stepping-Stone.Journal of Operational Research Society. 1989; 40(6):581– 90.
  • Charnes A, Cooper WW. The Stepping-Stone method for explaining linear programming calculations in transportation problems. Management Science. 1954;1(1):49–69.
  • Dantzig GB. Linear programming an extension.Princeton, NJ: Princeton University Press; 1963.
  • Dhose ED, Morrison KR. Using transportation solutions for a facility location problem. Computers and Industrial Engineering. 1996;31(1/2):63–6.
  • Gass SI. On solving the transportation problem. Journal of Operational Research Society. 1990;41(4):291–7.
  • Glover F, Karney D, Klingman D, Napier A. A computation study on start procedures, basis change criteria, and solution algorithms for transportation problems. Management Science. 1974;20(5):793–813.
  • Goyal SK. Improving VAM for unbalanced transportation problems. Journal of Operational Research Society.1984;35(12):1113–14.
  • Goyal SK. A note on a heuristic for obtaining an initial solution for the transportation problem. Journal of Operational Research Society. 1991;42(9):819–21.
  • Ji P,Ghu KF. A dual-matrix approach to the transportation problem. Asia- Pacific Journal of Operations Research.2002;19(1):35–45.
  • Kirca O,Satir A. A heuristic for obtaining an initial solution for the transportation problem. Journal of Operational Research Society. 1990;41(9):865–71.
  • Raghavendra BG, Mathirajan M. Optimal allocation of buses to depots — a case study. OPSEARCH. 1987;24(4):228– 39.
  • Ramakrishnan GS. An improvement to Goyal’s modified VAM for the unbalanced transportation problem. Journal of Operational Research Society. 1988;39(6):609–10.
  • Reinfeld NV, Vogel WR. Mathematical programming. Englewood Gliffs, New Jersey: Prentice-Hall; 1958.
  • Shafaat A, Goyal SK. Resolution of degeneracy in transportation problems. Journal of Operational Research Society.1988;39(4):411–13.
  • Shajma RRK, Sharma KD. A new dual based procedure for the transportation problem. European Journal of Operational Research. 2000;122:611–24.
  • Shih W. Modified stepping-stone method asa teaching aid for capacitated transportation problems. Decision Sciences.1987;18:662–76.
  • Shimshak DG, Kaslik JA, Barclay TD. A modification of Vogel’s approximation method through the use of heuristics.INEOR. 1981;19:259–63.
  • Sridharan R. Allocation of buses to depots: a case study. Vikalpa, The Journal for Decision Makers. 1991;16(2):27–32.
  • Sudhakar VJ, Arunsankar N, Karpagam. T(2012)a new approach for finding an optimal solution for transportation problems. European Journal of Scientific research. 2012; 68(2):254–7.
  • Vasudevan J, Malini E, Victor DJ. Fuelsavings in bus transit using depotterminal bus allocation model. Journal of Transport Management. 1993;17(7):409–16.

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.