A Hybrid Simple Additive Weighting Approach for Constrained Multicriteria Facilities Location Problem of Glass Production Industries Under Uncertainty

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.