Fuzzified AHP in the evaluation of scientific monographs

Fuzzification of the analytic hierarchy process (AHP) is of great interest to researchers since it is a frequently used method for coping with complex decision making problems. There have been many attempts to fuzzify the AHP. We focus particularly on the construction of fuzzy pairwise comparison matrices and on obtaining fuzzy weights of objects from them subsequently. We review the fuzzification of the geometric mean method for obtaining fuzzy weights of objects from fuzzy pairwise comparison matrices. We illustrate here the usefulness of the fuzzified AHP on a real-life problem of the evaluation of quality of scientific monographs in university environment. The benefits of the presented evaluation methodology and its suitability for quality assessment of R&D results in general are discussed. When the task of quality assessment in R&D is considered, an important role is played by peer-review evaluation. Evaluations provided by experts in the peer-review process have a high level of subjectivity and can be expected in a linguistic form. New decision-support methods (or adaptations of classic methods) well suited to deal with such inputs, to capture the consistency of experts’ preferences and to restrict the subjectivity to an acceptable level are necessary. A new consistency condition is therefore defined here to be used for expertly defined fuzzy pairwise comparison matrices.     

Non-extensive thermodynamics and stationary processes of localization

We focus our attention on dynamical processes characterized by an entropic index Q<1. According to the probabilistic arguments of Tsallis, C and Bukman, DJ [Phys Rev E 1996;54:R2197] these processes are subdiffusional in nature. The non-extensive generalization of the Kolmogorov–Sinai (KS) entropy yielding the same entropic index implies the stationary condition. We note, on the other hand, that enforcing the stationary property on subdiffusion has the effect of producing a localization process occurring within a finite time scale. We thus conclude that the stationary dynamic processes with Q<1 must undergo a localization process occurring at a finite time. We check the validity of this conclusion by means of a numerical treatment of the dynamics of the logistic map at the critical point.     

Maintaining convergence properties of BiCGstab methods in finite precision arithmetic

It is well-known that Bi-CG can be adapted so that hybrid methods with computational complexity almost similar to Bi-CG can be constructed, in which it is attempted to further improve the convergence behavior. In this paper we will study the class of BiCGstab methods.In many applications, the speed of convergence of these methods appears to be determined mainly by the incorporated Bi-CG process, and the problem is that the Bi-CG iteration coefficients have to be determined from the BiCGstab process. We will focus our attention to the accuracy of these Bi-CG coefficients, and how rounding errors may affect the speed of convergence of the BiCGstab methods. We will propose a strategy for a more stable determination of the Bi-CG iteration coefficients and by experiments we will show that this indeed may lead to faster convergence.     

Adaptive and nonadaptive approaches to statistically based methods for solving stochastic linear programs: a?computational investigation

Large scale stochastic linear programs are typically solved using a combination of mathematical programming techniques and sample-based approximations. Some methods are designed to permit sample sizes to adapt to information obtained during the solution process, while others are not. In this paper, we experimentally examine the relative merits and challenges of approximations based on adaptive samples and those based on non-adaptive samples. We focus our attention on Stochastic Decomposition (SD) as an adaptive technique and Sample Average Approximation (SAA) as a non-adaptive technique. Our results indicate that there can be minimal difference in the quality of the solutions provided by these methods, although comparing their computational requirements would be more challenging.     

Two-level hierarchically preconditioned conjugate gradient methods for solving linear elasticity finite element equations

In this paper we study and compare some preconditioned conjugate gradient methods for solving large-scale higher-order finite element schemes approximating two- and three-dimensional linear elasticity boundary value problems. The preconditioners discussed in this paper are derived from hierarchical splitting of the finite element space first proposed by O. Axelsson and I. Gustafsson. We especially focus our attention to the implicit construction of preconditioning operators by means of some fixpoint iteration process including multigrid techniques. Many numerical experiments confirm the efficiency of these preconditioners in comparison with classical direct methods most frequently used in practice up to now.     

Interactive optimization

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization.     

The forgotten sons: Warehousing systems for brick-and-mortar retail chains

Warehouses are an inevitable component in any supply chain and a vividly investigated object of research. Much attention, however, is absorbed by warehousing systems dedicated to the special needs of online retailers in the business-to-consumer segment. Due to the ever increasing sales volumes of e-commerce this focus seems self-evident, but a much larger fraction of retail sales are still realized by traditional brick-and-mortar stores. The special needs of warehouses servicing these stores are focused in this paper. While e-commerce warehouses face low-volume-high-mix picking orders, because private households tend to order just a few pieces per order from a large assortment, distribution centers of retail chains rather have to process high-volume-low-mix orders. We elaborate the basic requirements within both business segments and identify suited warehousing systems for brick-and-mortar stores (e.g., fully-automated case picking). The setup of each identified warehousing system is described, elementary decision problems are discussed, and the existing literature is surveyed. Furthermore, we identify future research needs.     

Interactive optimization

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/ machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization.     

Exponentially-fitted methods and their stability functions

We investigate the properties of stability functions of exponentially-fitted Runge–Kutta methods, and we show that it is possible (to some extent) to determine the stability function of a method without actually constructing the method itself. To focus attention, examples are given for the case of one-stage methods. We also make the connection with so-called integrating factor methods and exponential collocation methods. Various approaches are given to construct these methods.     

Computing the Pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixed-integer programming algorithm

In this article, we study the bi-level linear programming problem with multiple objective functions on the upper level (with particular focus on the bi-objective case) and a single objective function on the lower level. We have restricted our attention to this type of problem because the consideration of several objectives at the lower level raises additional issues for the bi-level decision process resulting from the difficulty of anticipating a decision from the lower level decision maker. We examine some properties of the problem and propose a methodological approach based on the reformulation of the problem as a multiobjective mixed 0–1 linear programming problem. The basic idea consists in applying a reference point algorithm that has been originally developed as an interactive procedure for multiobjective mixed-integer programming. This approach further enables characterization of the whole Pareto frontier in the bi-objective case. Two illustrative numerical examples are included to show the viability of the proposed methodology.     

Shedding vertices of vertex decomposable well-covered graphs

We focus our attention on well-covered graphs that are vertex decomposable. We show that for many known families of these vertex decomposable graphs, the set of shedding vertices forms a dominating set. We then construct three new infinite families of well-covered graphs, none of which have this property. We use these results to provide a minimal counterexample to a conjecture of Villarreal regarding Cohen–Macaulay graphs.     

Evolution equations of higher order in banach spaces

The present paper deals with a minimal extension of the classical semigroup theory for equations of any order in Banach spaces with closed densely defined linear operators as coefficients. We do not ask anymore from our operators than in the case of first-order equations, i.e., Semigroups. We present here a generalization of Myadera-Phillips--Feller theorem, of Hille theorem and some other results. The method is quite general. We focus our attention on a particular operator solution (main propagator or abstract initial value Green function) and we assume some properties about it. From this we can obtain all needed information about complementary operator solutions, among others.     

Euler-Lagrange and Hamiltonian formalisms in dynamic optimization

We consider dynamic optimization problems for systems governed by differential inclusions. The main focus is on the structure of and interrelations between necessary optimality conditions stated in terms of Euler-Lagrange and Hamiltonian formalisms. The principal new results are: an extension of the recently discovered form of the Euler-Weierstrass condition to nonconvex valued differential inclusions, and a new Hamiltonian condition for convex valued inclusions. In both cases additional attention was given to weakening Lipschitz type requirements on the set-valued mapping. The central role of the Euler type condition is emphasized by showing that both the new Hamiltonian condition and the most general form of the Pontriagin maximum principle for equality constrained control systems are consequences of the Euler-Weierstrass condition. An example is given demonstrating that the new Hamiltonian condition is strictly stronger than the previously known one.

     

Credit risk optimization using factor models

We study portfolio credit risk management using factor models, with a focus on optimal portfolio selection based on the tradeoff of expected return and credit risk. We begin with a discussion of factor models and their known analytic properties, paying particular attention to the asymptotic limit of a large, finely grained portfolio. We recall prior results on the convergence of risk measures in this “large portfolio approximation” which are important for credit risk optimization. We then show how the results on the large portfolio approximation can be used to reduce significantly the computational effort required for credit risk optimization. For example, when determining the fraction of capital to be assigned to particular ratings classes, it is sufficient to solve the optimization problem for the large portfolio approximation, rather than for the actual portfolio. This dramatically reduces the dimensionality of the problem, and the amount of computation required for its solution. Numerical results illustrating the application of this principle are also presented. JEL Classification G11     

D-optimal matrices via quadratic integer optimization

We show how to express the problem of searching for D-optimal matrices as a Linear and Quadratic Integer Optimization problem. We also focus our attention in the case where the size of the circulant submatrices that are used to construct a D-optimal matrix is a multiple of 3. In this particular case, we describe some additional combinatorial and number-theoretic characteristics that a solution of the D-optimal matrix problem must possess. We give some solutions for some quite challenging D-optimal matrix problems that can be used as benchmarks to test the efficiency of Linear and Quadratic Integer Optimization algorithms.     

A rich vehicle routing problem dealing with perishable food: a case study

This paper presents a successful application of operations research techniques in guiding the decision making process to achieve a superior operational efficiency in core activities. We focus on a rich vehicle routing problem faced by a Portuguese food distribution company on a daily basis. This problem can be described as a heterogeneous fleet site dependent vehicle routing problem with multiple time windows. We use the adaptative large neighbourhood search framework, which has proven to be effective to solve a variety of different vehicle routing problems. Our plans are compared against those of the company and the impact that the proposed decision support tool may have in terms of cost savings is shown. The algorithm converges quickly giving the planner considerably more time to focus on value-added tasks, rather than manually correct the routing schedule. Moreover, contrarily to the necessary adaptation time of the planner, the tool is quite flexible in following market changes, such as the introduction of new customers or new products.