A linear fractional transportation problem in uncertain environment is studied in this paper where the uncertain parameters of the problem are of belief degree—based uncertainty. For the first time, this type of uncertainty is considered for the linear fractional transportation problem. Belief degree—based uncertainty is useful for the cases that no historical information of an uncertain event is available. Zigzag type uncertainty distribution is used to show the belief degree—based uncertainty of the parameters of the problem. As solution methodology, the uncertain linear fractional transportation problem is converted to a crisp form using three approaches of expected value model, expected value and chance-constrained model, and chance-constrained model, separately. An extensive computational study on a real illustrative example shows the efficiency of the proposed formulation and the conversion approaches. The sensitivity analysis over the example illustrates the high dependency of the objective function value to the changes of the confidence level values of the chance constraints in the expected value and chance-constrained programming approach and the chance-constrained programming approach.

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.