A unified approach for fuzzy multiobjective stochastic programming with Cauchy and extreme value distributed fuzzy random variables

Parameter estimation and optimization of multi-objective capacitated stochastic transportation problem for gamma distribution

“…Every company makes use of different modes and routes of transportation for maximum profitability. A distribution department uses transportation to reduce the 22,19,21,18,20,22,18,20,23,20,21,20,20,19,18,19,18,19,20,22,21,18,20,19,22,18,21,21,19,20 a 2 14,16,15,14,16,15,16,15,14,17,16,15,17,12,16,16,17,14,15,16, 16,16,15,15,16,17,12,13,13,14 a 3 21,20,20,21,18,20,19,19,21,20,21,22,21,20,22,22,21,21,21,19,…”

“…Some techniques are based on statistical and probabilistic concepts for dealing stochastically with the problem and then finding the corresponding deterministic form. Some prominent work, that can be useful for the present study include, Sinha et al [1] used Joint Normal distribution; Sahoo and Biswal [2] used Cauchy and Extreme value distribution; Mahapatra et al [3] used Log-Normal distribution; Barik et al [4] used Pareto distribution; Roy and Mahapatra [5] used Log-Normal distribution with interval type parameters; Mahapatra et al [6] used Extreme Value distribution with multi-choice parameters; Roy et al [7] used Exponential distribution with multichoice parameters; Biswal and Samal [8] used Cauchy distribution with multi-choice parameters; Samal and Biswal [9] used Exponential distribution; Javaid et al [10] used Weibull distribution; Mahapatra et al [11] used Weibull distribution with multi choice parameters; Roy [12] used Weibull distribution with multi-choice parameters; Barik [13] used Pareto distribution; Roy [14] used Logistic distribution with multichoice parameters; Biswas and De [15] used Joint Extreme value distribution with fuzzy parameters; Barik and Biswal [16] used Normal distribution; Maity et al [17] used Normal distribution; De et al [18] used Cauchy and Extreme value distribution with fuzzy parameters; Acharya et al [19] used three-parameter extreme value distribution for getting the equivalent deterministic form of the uncertain stochastic parameter and also all of them formulated same type of linear TP distribution. Dufuaa and Sultan [20] formulated the maintenance planning problem by considering the schedule reserves scenario with sufficient resources to meet emergency employment when preparing a schedule for onthe-spot employment.…”