Multi-objective stochastic transportation problem involving three-parameter extreme value distribution

Authors

  • Mitali Madhumita Acharya KIIT University, School of Applied Sciences, Department of Mathematics, Bhubaneswar, Odisha, India
  • Adane Abebaw Gessesse KIIT University, School of Applied Sciences, Department of Mathematics, Bhubaneswar, Odisha, India
  • Rajashree Mishra KIIT University, School of Applied Sciences, Department of Mathematics, Bhubaneswar, Odisha, India
  • Srikumar Acharya KIIT University, School of Applied Sciences, Department of Mathematics, Bhubaneswar, Odisha, India

DOI:

https://doi.org/10.2298/YJOR180615036A

Keywords:

multi-objective programming, stochastic programming problem, transportation problem, extreme value distribution, ε-constraint method

Abstract

In this paper, we considered a multi-objective stochastic transportation problem where the supply and demand parameters follow extreme value distribution having three-parameters. The proposed mathematical model for stochastic transportation problem cannot be solved directly by mathematical approaches. Therefore, we converted it to an equivalent deterministic multi-objective mathematical programming problem. For solving the deterministic multi-objective mathematical programming problem, we used an ε-constraint method. A case study is provided to illustrate the methodology.

References

Biswal, M.P., Sahoo, N.P. and Duan, L., “Probabilistic linear programming problems with exponential random variables: A technical note”, European Journal of Operational Research, 111-3 (1998) 589-597.

Biswal, M.P. and Samal, H.K., “Stochastic transportation problem with Cauchy random variables and multi-choice parameters”, Vidyasagar University, Midnapore, West-Bengal, India, 2013.

Sahoo, N.P. and Duan, L., “Probabilistic linearly constrained programming problems with lognormal random variables”, Opsearch, 42-1 (2005) 70-76.

Charnes, A., Cooper, W.W. and Symonds, G.H., “Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil”, Management Science, 4-3 (1958) 235-263.

Chavez, H., Krystel, K.C., Luis, H. and Agustn, B., “Simulation-based multi-objective model for supply chains with disruptions in transportation”, Robotics and Computer-Integrated Manufacturing, 43 (2017) 39-49.

Dantzig, G.B., “Linear programming under uncertainty”, In Stochastic programming, 2010, 111.

Goicoechea, A. and Lucien, D., “Nonnormal deterministic equivalents and a transformation in stochastic mathematical programming”, Applied Mathematics and Computation, 21-1 (1987) 51-72.

Hulsurkar, S., Biswal, M.P. and Surabhi, B.S., “Fuzzy programming approach to multi-objective stochastic linear programming problems”, Fuzzy Sets and Systems, 88-2 (1997) 173-181.

Jagannathan, R., “Chance-constrained programming with joint constraints”, Operations Research, 22-2 (1974) 358-372.

Kotz, S. and Nadarajah, S., “Extreme value distributions: theory and applications”, World Scientific, 2000.

Krishnamoorthy, K., “Handbook of statistical distributions with applications”, CRC Press, 2016.

Kudjo, N.B.B., “The Transportation Problem: Case Study of Coca Cola Bottling Company Ghana”, PhD thesis, 2013.

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

Mahapatra, D.R., Roy, S.K. and Biswal, M.P., “Stochastic based on multi-objective transportation problems involving normal randomness”, Advanced Modeling and Optimization, 12-2 (2010) 205-223.

Miller, B.L. and Harvey, M.W., “Chance constrained programming with joint constraints”, Operations Research, 13-6 (1965) 930-945.

Mousa, A.A., Hamdy, M.G. and Adel, Y.E., “Efficient evolutionary algorithm for solving multi-objective transportation problem”, Journal of Natural Sciences and Mathematics, 4-1 (2010) 77-102.

Parsons, B.L. and Lal, M., “Distribution parameters for flexural strength of ice”, Cold Regions Science and Technology, 19-3 (1991) 285-293.

Quddoos, A., Ull Hasan, M.G. and Khalid, M.M., “Multichoice stochastic transportation problem involving general form of distributions”, SpringerPlus, 3-1 (2014) 565.

Roy, S.K., “Multi-choice stochastic transportation problem involving Weibull distribution”, International Journal of Operational Research, 21-1 (2014) 38-58.

Roy, S.K., Ebrahimnejad, A., Verdegay, J.L. and Das, S., “New approach for solving intuitionistic fuzzy multi-objective transportation problem”, Sadhana, 43-1 (2018) 3.

Roy, S.K., Mahapatra, D.R. and Biswal, M.P., “Multi-choice stochastic transportation problem with exponential distribution”, Journal of Uncertain Systems, 6-3 (2012) 200-213.

Roy, S.K. and Mahapatra, D.R., “Multi-objective interval-valued transportation probabilistic problem involving log-normal”, International Journal of Mathematics and Scientific Computing, 1-2 (2011) 14-21.

Roy, S.K., Maity, G., Gerhard, W.W. and Gok, S.Z.A., “Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal”, Annals of Operations Research, 253-1 (2017) 599-620.

Sahoo, N.P. and Biswal, M.P., “Computation of some stochastic linear programming problems with Cauchy and extreme value distributions”, International Journal of Computer Mathematics, 82-6 (2005) 685-698.

Schrage, L.E., “Optimization modeling with LINGO”, Lindo System, 2006.

Singh, V.P., “Generalized extreme value distribution”, In Entropy-based parameter estimation in hydrology, (Springer, 1998) 169-183.

Williams, A.C., “A stochastic transportation problem”, Operations Research, 11-5 (1963) 759-770.

Yeola, M.C. and Jahav, V.A., “Solving multi-objective transportation problem using fuzzy programming technique-parallel method”, 2016.

Zaki, S.A., Mousa, A.A.A., Geneedi, H.M. and Elmekawy, A.Y., “Efficient multiobjective genetic algorithm for solving transportation, assignment, and transshipment problems”, Applied Mathematics, 3-1 (2012) 92.

Zangiabadi, M. and Maleki, H.R., “Fuzzy goal programming for multiobjective transportation problems”, Journal of Applied Mathematics and Computing, 24-1&2 (2007) 449-460.

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Published

2019-08-01

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Section

Research Articles