Multi-choice stochastic transportation problem involving weibull distribution


  • Deshabrata Roy Mahapatra



Multi-choice Programming, Stochastic Programming, Weibull Distribution, Transporta- tion Problem, Transformation Technique, Mixed-integer Programming.


A solution procedure for multi-choice stochastic transportation problem is presented here
with some stochastic constraints containing parameters as supply and demand of Weibull distribution
and cost coecients of objective function have multi-choice in nature of real life situation. At rst, all
stochastic constraints are transformed into deterministic constraints by using the stochastic approach.
A transformation technique is introduced for manipulation of multi-choice cost coecients of objective
function into equivalent deterministic form in terms of binary variables with additional restrictions.
The auxiliary and additional constraints involving binary variables depend upon the set of consecutive
terms of cost coecients of the objective function whose sum is equal or nearer to the aspiration levels.
Finally, a numerical example is presented to illustrate the solution procedure of the specied proposed


Acharya, S and Acharya, M.M., Generalized transformation technique for multi-choice linear programming problem. An International Journal of Optimization and Control:Theories & Applications, 3(1), 45-54 (2013).

Biswal, M.P. and Acharya, S., Transformation of a multi-choice linear programming problem. Applied Mathematics and Computation, 210, 182-188 (2009). CrossRef

Biswal, M.P. and Acharya, S., Solving probabilistic programming problems involving multi-choice parameters. Opsearch, 210, 1-19 (2011).

Chang, C.-T., Multi-choice goal programming. Omega, The International Journal of Management Science., 35, 389-396 (2007).

Chang, C.-T., Binary fuzzy programming. European Journal of Operation Research, 180, 29-37 (2007). CrossRef

Chang, C.-T., Revised multi-choice goal programming. Applied Mathematical Modeling, 32, 2587-2595 (2008). CrossRef

Chang, Ching-Ter, Chen, Huang-Mu , and Zhuang, Zheng-Yun, Multi-coefficients goal programming. Computers and Industrial Engineering, 62(2), 616-623 (2012). CrossRef

Liao, Chin-Nung, Revised multi-segment goal programming and applications. Prob. Stat. Forum, 4, 110-119 (2011).

Fok, S.L. and Smart, J., Accuracy of failure predictions based on weibull statistic. J. Eur. Ceram. Soc., 15, 905-908 (1995). CrossRef

Goicoechea, A., Hansen, D.R. and Duckstein, L., Multi-objective Decision Analysis with Engineering and Business Application. New York: John Wiley and Sons (1982).

Hitchcock, F.L., The distribution of a product from several sources to numerous localities. J. Math. Physics, 20, 224-230 (1941).

Koopmans, T.C., Optimum utilization of the transportation system. Ecpnometrica, 17, 3-4 (1949).

Mahapatra, D.R., Roy, S.K. and Biswal, M.P., Computation of multi-objective stochastic transportation problem involving normal distribution with joint constraints. The Journal of Fuzzy Mathematics. 19(4), 865-876 (2011).

Mahapatra, D.R., Roy, S.K. and Biswal, M.P., Multi-choice stochastic transportation problem involving extreme value distribution. Applied Mathematical Modelling, 37(4), 2230-2240 (2013). CrossRef

Rabindran, A., Philips, D.T. and Solberg, J.J., Operations Research; Principles and Practice. Second Edition, New York: John Wiley and Sons (1987).

Schrage, L., Optimization Modeling with LINGO. LINDO System, Chicago, I11, USA, 6th edition.

Weibull, W., A statistical distribution function of wide applicability. J. of Appl. Mach., 15, 293-302 (1951).




How to Cite

Mahapatra, D. R. (2013). Multi-choice stochastic transportation problem involving weibull distribution. An International Journal of Optimization and Control: Theories &Amp; Applications (IJOCTA), 4(1), 45–55.



Optimization & Applications