This paper presents the study of a multichoice multiobjective transportation problem (MCMOTP) when at least one of the objectives has multiple aspiration levels to achieve, and the parameters of supply and demand are random variables which are not predetermined. The random variables shall be assumed to follow extreme value distribution, and the demand and supply constraints will be converted from a probabilistic case to a deterministic one using a stochastic approach. A transformation method using binary variables reduces the MCMOTP into a multiobjective transportation problem (MOTP), selecting one aspiration level for each objective from multiple levels. The reduced problem can then be solved with goal programming. The novel adapted approach is significant because it enables the decision maker to handle the many objectives and complexities of real-world transportation problem in one model and find an optimal solution. Ultimately, a mixed-integer mathematical model has been formulated by utilizing GAMS software, and the optimal solution of the proposed model is obtained. A numerical example is presented to demonstrate the solution in detail.

中文翻译：

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具有极值分布的多选择多目标随机运输问题的目标规划方法

本文提出了一种多目标多目标运输问题（MCMOTP）的研究，当至少一个目标具有多个期望水平且供需参数是不确定的随机变量时。应假定随机变量遵循极值分布，并且将使用随机方法将需求和供应约束条件从概率情况转换为确定性情况。使用二进制变量的转换方法将MCMOTP简化为多目标运输问题（MOTP），从多个级别中为每个目标选择一个期望级别。减少的问题然后可以通过目标编程解决。新颖的适应方法非常重要，因为它使决策者能够在一个模型中处理现实运输问题的许多目标和复杂性，并找到最佳解决方案。最终，利用GAMS软件建​​立了一个混合整数数学模型，并获得了该模型的最优解。给出了一个数值示例，以详细说明该解决方案。