Transportation problem is the prominent class of mathematical programming problems that has a significant role in many practical transportation fields. Naturally, the transportation parameters inherently involve uncertainty in real life caused by lacking of information, imprecision in judgment, environmental factors, and etc. Therefore, it is very valuable to handle transportation problem under uncertainty aspect. The aim of this paper is to study the solution of the rough multi-objective transportation problem by supposing that the decision makers realize the transportation cost, availability and demand of the product as rough interval coefficients. The proposed approach exploits the merits of the weighted sum method to find the non-inferior solutions and it has two distinguishing features. Firstly, the proposed approach characterizes the surely Pareto optimal solution through converting the lower interval into two crisp transportation problems. Secondly, the proposed approach characterizes the possibly Pareto optimal solution through decomposing the upper interval into two crisp transportation problems. Furthermore, the expected nondominated value is applied to obtain the optimal compromise solutions of multi-objective transportation problem in rough environment. The presented approach is showed with rough multi-objective optimization problem as numerical illustration, where a wide set of the expected compromise solution ranged from 15.75 to 25.8 can be obtained. Furthermore, the investigation on the rough multi-objective transportation problem is conducted a real thought-provoking case study, where the optimal rough interval of transportation cost ranged from 97 to 314 can be achieved. With the adoption of rough environment modeling, a wide variate of optimal solutions can be achieved that can help the decision maker to extract the best compromise alternative according to practical situations. This represents a novel contribution to the decision making field and profit satisfaction models.

运输问题是数学编程问题的重要一类，在许多实际的运输领域中都发挥着重要作用。自然地，运输参数固有地会由于缺乏信息，判断不准确，环境因素等而导致现实生活中存在不确定性。因此，在不确定性方面处理运输问题非常有价值。本文的目的是通过假设决策者将产品的运输成本，可获得性和需求作为粗糙区间系数来实现，从而研究粗糙的多目标运输问题的解决方案。所提出的方法利用加权和方法的优点来找到非劣解，它具有两个明显的特点。首先，所提出的方法通过将较低的区间转换为两个清晰的运输问题来表征肯定的Pareto最优解。其次，所提出的方法通过将上限区间分解为两个清晰的运输问题来表征可能的帕累托最优解。此外，将期望的非支配值应用于在恶劣环境下获得多目标运输问题的最优折衷解。给出的方法以粗略的多目标优化问题作为数值表示，可以从15.75到25.8的范围内获得广泛的预期折衷解决方案。此外，针对粗糙的多目标运输问题进行了调查，并进行了真正的发人深省的案例研究，可以实现的最佳运输成本的粗略区间为97到314。通过采用粗糙的环境建模，可以实现各种各样的最佳解决方案，这些解决方案可以帮助决策者根据实际情况提取最佳折衷方案。这代表了对决策领域和利润满意度模型的新颖贡献。