The transportation problem in real life is an uncertain problem with multi-objective decision-making. In particular, by considering the conflicting objectives/criteria such as transportation costs, transportation time, discount costs, labour costs, damage costs, decision maker searches for the best transportation set-up to find out the optimum shipment quantity subject to certain capacity restrictions on each route. In this paper, capacitated stochastic transportation problem is formulated as a multi-objective optimization model along with some capacitated restrictions on the route. In the formulated problem, we assume that parameters of the supply and demand constraints’ follow gamma distribution, which is handled by the chance constrained programming approach and the maximum likelihood estimation approach has been used to assess the probabilistic distributions of the unknown parameters with a specified probability level. Furthermore, some of the objective function’s coefficients are consider as ambiguous in nature. The ambiguity in the formulated problem has been presented by interval type 2 fuzzy parameter and converted into the deterministic form using an expected value function approach. A case study on transportation illustrates the computational procedure.

现实生活中的运输问题是一个多目标决策的不确定性问题。特别是，通过考虑相互矛盾的目标/标准，例如运输成本，运输时间，折扣成本，人工成本，损坏成本，决策者将搜索最佳运输设置，以找到最佳运输数量，但要满足某些运输能力限制。每条路线。在本文中，将有能力的随机运输问题与一些受能力限制的路线一起，制定为多目标优化模型。在提出的问题中，我们假设供求约束的参数遵循伽玛分布，它由机会约束编程方法处理，最大似然估计方法已用于评估具有指定概率水平的未知参数的概率分布。此外，某些目标函数的系数本质上被认为是模棱两可的。区间问题2的模糊参数表示了所提出问题的歧义性，并使用期望值函数方法将其转换为确定性形式。一个关于运输的案例说明了计算过程。区间问题2的模糊参数表示了所提出问题的歧义性，并使用期望值函数方法将其转换为确定性形式。一个关于运输的案例说明了计算过程。区间问题2的模糊参数表示了所提出问题的歧义性，并使用期望值函数方法将其转换为确定性形式。一个关于运输的案例说明了计算过程。