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The data envelopment analysis (DEA) treats decision-making units (DMUs) as black boxes: there is an unknown internal structure and transformation mechanism of input to output. Two-stage models have been proposed to resolve this problem by considering the internal structure of DMUs. However, each DMU has a different structure, and in two-stage models, the poor estimation of sub-models causes conflicts in the intermediate layer. Therefore, it is necessary to use additional tools to extract insight into opportunities to enhance the performance of DMUs. This paper presents a three-stage model employing DEA to evaluate efficiency, a Tobit regression model to identify the determinants, and a neural network (NN) to improve those determinants. Improvement in the determinants of a DMU enhances its efficiency. The developed model is applied to the empirical dataset of commercial banks from the countries that have joined the belt and road initiative (BRI), grouping them based on their economist intelligence unit (EIU) rating. The results provide valuable information on the efficiency enhancement process for banks to benefit from the BRI.

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Based on the classical Markowitz model, we formulate a vector (multicriteria) Boolean problem of portfolio optimization with bottleneck criteria under risk. We obtain the lower and upper attainable bounds for the quantitative characteristics of the type of stability of the problem, which is a discrete analog of the Hausdorff upper semicontinuity of the multivalued mapping that defines the Pareto optimality. INTRODUCTIONCurrently, there has been considerable interest in multiobjective decision-making under uncertainty and risk (problems of game theory, mathematical economy, optimal control, investment analysis, bank sector, insurance business, etc.). The wide use of discrete optimization models has attracted the attention of many experts to various aspects of stability and problems of parametric and postoptimal analysis of both scalar (single-criterion), and vector (multicriteria) discrete optimization (the monographs [1-3], reviews [4][5][6], and annotated bibliographies [7,8]).One of the well-known approaches to the stability analysis of vector discrete optimization problems is focused on obtaining quantitative characteristics of the stability and consists in finding an ultimate level of perturbations of the initial data of the problem that do not result in new Pareto optimal solutions. The majority of the results in this field is related to deriving formulas or estimates for the stability radius of vector problems of Boolean and integer programming with linear criteria [6,[9][10][11][12]. In the present paper, we will obtain the lower-and upper-bound attainable estimates for the stability radius of a vector Boolean problem with bottleneck criteria, i.e., of a portfolio optimization problem with Savage's minimax risk criteria. (The results of this paper were partially announced in [13].) PROBLEM STATEMENT AND MAIN DEFINITIONS