Design of an Analysis Model for Strategic Behavior in the Digital Economy

Nowadays, multi-criteria decision-making techniques are highly developed, and are widely applied in multiple fields. They model and solve decisional problems by optimising multiple conflicting objectives. These techniques are very useful because they simultaneously analyse all the different criteria, and select the best alternatives according to the decision-maker’s objectives and preferences. An important issue in this context is the adequacy of the structure of corporate long-term financing and its potential impact on the sustainable development of the long-term business plan. The purpose of this study is to advance the analysis of these strategic decisions, measuring the a posteriori results and analysing their coherence with the strategies followed a priori. To do this, sustainable strategic decisions will be mathematically modelled and parametrised, creating a system to study the preferences followed and to describe the corporate behaviour. This system is applied as a case example for two leading companies in the digital sector, and the corresponding results over the last few years are evaluated

Using Non-Additive Measure for Optimization-Based Nonlinear Classification

Over the past few decades, numerous optimization-based methods have been proposed for solving the classification problem in data mining. Classic optimization-based methods do not consider attribute interactions toward classification. Thus, a novel learning machine is needed to provide a better understanding on the nature of classification when the interaction among contributions from various attributes cannot be ignored. The interactions can be described by a non-additive measure while the Choquet integral can serve as the mathematical tool to aggregate the values of attributes and the corresponding values of a non-additive measure. As a main part of this research, a new nonlinear classification method with non-additive measures is proposed. Experimental results show that applying non-additive measures on the classic optimization-based models improves the classification robustness and accuracy compared with some popular classification methods. In addition, motivated by well-known Support Vector Machine approach, we transform the primal optimization-based nonlinear classification model with the signed non-additive measure into its dual form by applying Lagrangian optimization theory and Wolfes dual programming theory. As a result, 2 – 1 parameters of the signed non-additive measure can now be approximated with m (number of records) Lagrangian multipliers by applying necessary conditions of the primal classification problem to be optimal. This method of parameter approximation is a breakthrough for solving a non-additive measure practically when there are a relatively small number of training cases available (). Furthermore, the kernel-based learning method engages the nonlinear classifiers to achieve better classification accuracy. The research produces practically deliverable nonlinear models with the non-additive measure for classification problem in data mining when interactions among attributes are considered

MCDM approach to evaluating bank loan default models

Banks and financial institutions rely on loan default prediction models in credit risk management. An important yet challenging task in developing and applying default classification models is model evaluation and selection. This study proposes an evaluation approach for bank loan default classification models based on multiple criteria decision making (MCDM) methods. A large real-life Chinese bank loan dataset is used to validate the proposed approach. Specifically, a set of performance metrics is utilized to measure a selection of statistical and machine-learning default models. The technique for order preference by similarity to ideal solution (TOPSIS), a MCDM method, takes the performances of default classification models on multiple performance metrics as inputs to generate a ranking of default risk models. In addition, feature selection and sampling techniques are applied to the data pre-processing step to handle high dimensionality and class unbalancedness of bank loan default data. The results show that K-Nearest Neighbor algorithm has a good potential in bank loan default prediction

Solution Techniques for Classes of Biobjective and Parametric Programs

Mathematical optimization, or mathematical programming, has been studied for several decades. Researchers are constantly searching for optimization techniques which allow one to de-termine the ideal course of action in extremely complex situations. This line of scientific inquiry motivates the primary focus of this dissertation — nontraditional optimization problems having either multiple objective functions or parametric input. Utilizing multiple objective functions al-lows one to account for the fact that the decision process in many real-life problems in engineering, business, and management is often driven by several conflicting criteria such as cost, performance, reliability, safety, and productivity. Additionally, incorporating parametric input allows one to ac-count for uncertainty in models’ data, which can arise for a number of reasons, including a changing availability of resources, estimation or measurement errors, or implementation errors caused by stor-ing data in a fixed precision format. However, when a decision problem has either parametric input or multiple objectives, one cannot hope to find a single, satisfactory solution. Thus, in this work we develop techniques which can be used to determine sets of desirable solutions. The two main problems we consider in this work are the biobjective mixed integer linear program (BOMILP) and the multiparametric linear complementarity problem (mpLCP). BOMILPs are optimization problems in which two linear objectives are optimized over a polyhedron while restricting some of the decision variables to be integer. We present a new data structure in the form of a modified binary tree that can be used to store the solution set of BOMILP. Empirical evidence is provided showing that this structure is able to store these solution sets more efficiently than other data structures that are typically used for this purpose. We also develop a branch-and-bound (BB) procedure that can be used to compute the solution set of BOMILP. Computational experiments are conducted in order to compare the performance of the new BB procedure with current state-of-the-art methods for determining the solution set of BOMILP. The results provide strong evidence of the utility of the proposed BB method. We also present new procedures for solving two variants of the mpLCP. Each of these proce-dures consists of two phases. In the first phase an initial feasible solution to mpLCP which satisfies certain criteria is determined. This contribution alone is significant because the question of how such an initial solution could be generated was previously unanswered. In the second phase the set of fea-sible parameters is partitioned into regions such that the solution of the mpLCP, as a function of the parameters, is invariant over each region. For the first variant of mpLCP, the worst-case complex-ity of the presented procedure matches that of current state-of-the-art methods for nondegenerate problems and is lower than that of current state-of-the-art methods for degenerate problems. Addi-tionally, computational results show that the proposed procedure significantly outperforms current state-of-the-art methods in practice. The second variant of mpLCP we consider was previously un-solved. In order to develop a solution strategy, we first study the structure of the problem in detail. This study relies on the integration of several key concepts from algebraic geometry and topology into the field of operations research. Using these tools we build the theoretical foundation necessary to solve the mpLCP and propose a strategy for doing so. Experimental results indicate that the presented solution method also performs well in practice