In existence of interval-valued parameters and managerial limitations, multicriteria decision-making (MCDM) problems become more complex than their original situation. In such complex cases, the classical MCDM solution methods mainly cannot handle the managerial constraints of the problem and, therefore, become useless. This paper focuses on an MCDM problem such as establishment of the branches of a glass production company in all districts (provinces) of Iran in existence of interval-valued parameters and some managerial limitations like total available budget, number of selected branches for establishment, etc. To overcome the aforementioned difficulties, a novel modified version of the simple additive weighting method, which is of the well-known MCDM approaches of the literature, is formulated as a mixed integer linear formulation. The novelty of this formulation can be summarized by the following points: 1) to cope with the interval values of the criteria; 2) to keep the possibility of selecting a set of best locations among all possible locations; and 3) to handle the managerial limitations of the problem. The proposed formulation is validated by the real data of the case study, and its sensitivity is studied in detail. Finally, the performance of the proposed approach is compared to an alternative proposed solution approach.

中文翻译：

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不确定条件下玻璃生产行业受限多标准设施选址问题的混合简单加法加权方法

由于存在区间值参数和管理限制，多标准决策 (MCDM) 问题变得比原始情况更复杂。在这种复杂的情况下，经典的 MCDM 解决方法主要无法处理问题的管理约束，因此变得毫无用处。本文重点讨论 MCDM 问题，例如在伊朗所有地区（省）建立玻璃生产公司的分支机构，存在区间值参数和一些管理限制，如总可用预算、选定分支机构的数量等. 为克服上述困难，文献中众所周知的 MCDM 方法的简单加法加权方法的新修改版本被公式化为混合整数线性公式。该公式的新颖性可以概括为以下几点： 1）应对准则的区间值；2) 保持在所有可能位置中选择一组最佳位置的可能性；3) 处理问题的管理限制。所提出的公式得到了案例研究的真实数据的验证，并对其敏感性进行了详细研究。最后，将所提出的方法的性能与所提出的备选解决方案方法进行比较。并对其敏感性进行了详细研究。最后，将所提出的方法的性能与所提出的替代解决方案方法进行比较。并对其敏感性进行了详细研究。最后，将所提出的方法的性能与所提出的替代解决方案方法进行比较。