Exponential stability criteria of uncertain systems with multiple time delays

The exponential stability (with convergence rate α) of uncertain linear systems with multiple time delays is studied in this paper. Using the characteristic function of linear time-delay system, stability criteria are derived to guarantee α-stability. Sufficient conditions are also obtained for exponential stability of uncertain parametric systems with multiple time delays. For two-dimensional time-invariant system with multiple time delays, the proposed stability criteria are shown to be less conservative than those in the literature. Numerical examples are given to illustrate the validity of our new stability criteria.     

Multiattribute electronic procurement using goal programming

One of the key challenges of current day electronic procurement systems is to enable procurement decisions transcend beyond a single attribute such as cost. Consequently, multiattribute procurement have emerged as an important research direction. In this paper, we develop a multiattribute e-procurement system for procuring large volume of a single item. Our system is motivated by an industrial procurement scenario for procuring raw material. The procurement scenario demands multiattribute bids, volume discount cost functions, inclusion of business constraints, and consideration of multiple criteria in bid evaluation. We develop a generic framework for an e-procurement system that meets the above requirements. The bid evaluation problem is formulated as a mixed linear integer multiple criteria optimization problem and goal programming is used as the solution technique. We present a case study for which we illustrate the proposed approach and a heuristic is proposed to handle the computational complexity arising out of the cost functions used in the bids.     

具变时滞的非线性退化微分系统的渐近稳定性判据

In this paper, the asymptotic stability for singular differential nonlinear systems with multiple time-varying delays is considered. The V-functional method for general singular differential delay system is investigated. The asymptotic stability criteria for singular differential nonlinear systems with multiple time-varying delays are derived based on V-functional method and some analytical techniques, which are described as matrix equations or matrix inequalities. The results obtained are computationally flexible and efficient.     

Dynamic multiple criteria decision making in changeable spaces: from habitual domains to innovation dynamics

Human behaviors involve dynamic, evolving, interactive and adaptive processes. Important decision makings usually are dynamic, involving multiple criteria in changeable spaces. This article introduces the behavior mechanism that integrates the findings of neural science, psychology, system science, optimization theory and multiple criteria decision making. It shows how our brain and mind operate and describes our behaviors and decision making as dynamic processes of multiple criteria decision making in changeable spaces. Unless extraordinary events occur or special effort exerted, the dynamic processes will be stabilized in certain domains, known as Habitual Domains. Habitual Domains, which play a vital role in upgrading the quality of our decision making and lives, will be explored. In addition, as important consequential derivatives, concepts of Competence Set Analysis and Innovation Dynamics will also be discussed. Note that these concepts involve transitions between dynamic and static states.     

The design of multiactivity multifacility systems

We consider a service/distribution system in which each of N activities is to be carried out at one or several facility locations. Each activity is to be assigned to one out of a specified set of configurations; each configuration is a specific subset of the set of L facilities being considered, along with a specific strategy for their use. We call such a system a multiactivity multifacility system and present a mathematical formulation for its optimal design that includes capacity restrictions at the facilities and the treatment of multiple criteria. The design problem is simply to choose an appropriate configuration for each of the N activities. We discuss various criteria, and we show that the multiactivity multifacility design problem includes many familiar discrete location problems as special cases. We introduce a 0–1 linear optimization model called the Team Generalized Assignment Problem (T-GAP) and show that parametric solution of a T-GAP will yield all efficient solutions of the multiactivity multifacility design problem with multiple criteria. Rather than attempting to find all efficient solutions, however, we advocate an interactive approach and describe an interactive branch-and-bound algorithm that solves the design problem as a finite sequence of T-GAP's.     

Exponential stability of singularly perturbed switched systems with time delay

This paper investigates exponential stability of singularly perturbed switched systems with time delay. The multiple Lyapunov functions technique and dwell time approach are used to establish stability criteria for a switched system consisting of both stable and unstable subsystems. Examples are presented to illustrate the criteria.     

Management of multicriteria inventory classification

The most common method that materials managers use for classifying inventory items for planning and control purposes is the annual-dollar-usage ranking method (ABC classification). Recently, it has been suggested that multiple criteria ABC classification can provide a more comprehensive managerial approach, allowing consideration of other criteria such as lead time and criticality. This paper proposes the use of the Analytical Hierarchy Process (AHP) to reduce these multiple criteria to a univariate and consistent measure to consider multiple inventory management objectives.     

Delay-dividing approach for absolute stability of Lurie control system with mixed delays

This paper studies the absolute stability problem for a Lurie control system with nonlinearity located in an infinite sector and finite one. By dividing the discrete delay interval into multiple segments and choosing proper Lyapunov functionals, some delay dependent stability criteria are derived to guarantee the stability of the Lurie control system. It is established theoretically that the criteria are less conservative than the previous ones. Numerical examples demonstrate the validity of the proposed criteria.     

Enumeration and interactive selection of efficient paths in a multiple criteria graph for scheduling an earth observing satellite

We consider a satellite following orbits around the earth in order to take shots corresponding to images requested by various customers. The daily operations of such a satellite consist of defining a feasible and satisfactory shot sequence. This problem involves both combinatorial and multiple criteria difficulties. Indeed, the number of feasible shot sequences grows significantly with the number of images asked for, and the evaluation of a shot sequence is based on several conflicting criteria. We propose to formulate this problem as the selection of a multiple criteria path in a graph without circuit. Our approach for solving this problem involves two stages: generation of efficient paths and selection of a satisfactory path using a multiple criteria interactive procedure.     

Integer Programming Duality in Multiple Objective Programming

The weighted sums approach for linear and convex multiple criteria optimization is well studied. The weights determine a linear function of the criteria approximating a decision makers overall utility. Any efficient solution may be found in this way. This is not the case for multiple criteria integer programming. However, in this case one may apply the more general e-constraint approach, resulting in particular single-criteria integer programming problems to generate efficient solutions. We show how this approach implies a more general, composite utility function of the criteria yielding a unified treatment of multiple criteria optimization with and without integrality constraints. Moreover, any efficient solution can be found using appropriate composite functions. The functions may be generated by the classical solution methods such as cutting plane and branch and bound algorithms.     

Benchmarking in a multiple criteria performance context: An application and a conceptual framework

This article presents a conceptual benchmarking framework which applies a multiple criteria approach to assess performance. In the process, a multiple criteria procedure is used to assess the performance of three hundred and ninety two (392) Portuguese firms. Based on the results of this procedure, a conceptual framework is devised to facilitate addressing relevant benchmarking implications. The framework is designed to provide a conceptual linkage between the performance measurement methodology and the organizational benchmarking system.     

Criteria and dimension reduction of linear multiple criteria optimization problems

Two of the main approaches in multiple criteria optimization are optimization over the efficient set and utility function program. These are nonconvex optimization problems in which local optima can be different from global optima. Existing global optimization methods for solving such problems can only work well for problems of moderate dimensions. In this article, we propose some ways to reduce the number of criteria and the dimension of a linear multiple criteria optimization problem. By the concept of so-called representative and extreme criteria, which is motivated by the concept of redundant (or nonessential) objective functions of Gal and Leberling, we can reduce the number of criteria without altering the set of efficient solutions. Furthermore, by using linear independent criteria, the linear multiple criteria optimization problem under consideration can be transformed into an equivalent linear multiple criteria optimization problem in the space of linear independent criteria. This equivalence is understood in a sense that efficient solutions of each problem can be derived from efficient solutions of the other by some affine transformation. As a result, such criteria and dimension reduction techniques could help to increase the efficiency of existing algorithms and to develop new methods for handling global optimization problems arisen from multiple objective optimization.     

Absolute stability analysis of Lurie control system with multiple delays: An integral-equality approach

This paper investigates the stability problem for the nominal and uncertain Lurie control system with multiple delays, respectively. With the delay divided into two segments, a novel Lyapunov functional is introduced and some new delay-dependent stability criteria are derived by employing integral-equality technique. It is theoretically proved that the obtained criteria are less conservative than some existing ones. Two examples are given to illustrate the effectiveness of the proposed results.     

Lyapunov function of general Lurie systems with multiple nonlinearities

In this paper, the absolute stability problem of general Lurie control system with multiple nonlinearities is investigated. Some new necessary and sufficient conditions are obtained for the existence of Lyapunov function of extended Lurie form with negative definite and negative semidefinite derivatives. From these conditions, some very general algebraic criteria for absolute stability are obtained, which extend and generalize previous work on the subject. A numerical example is presented to illustrate the effectiveness of the new criteria.     

An effective Markov based approach for calculating the Limit Matrix in the analytic network process

Analytic network process is a multiple criteria decision analysis (MCDA) method that aids decision makers to choose among a number of possible alternatives or prioritize the criteria for making a decision in terms of importance. It handles both qualitative and quantitative criteria, that are compared in pairs, in order to forge a best compromise answer according to the different criteria and influences involved. The method has been widely applied and the literature review reveals a rising trend of ANP-related articles. The ‘power’ matrix method, a procedure necessary for the stability of the decision system, is one of the critical calculations in the mathematical part of the method. The present study proposes an alternative mathematical approach that is based on Markov chain processes and the well-known Gauss-Jordan elimination. The new approach obtains practically the same results as the power matrix method, requires slightly less time and number of calculations and handles effectively cyclic supermatrices, optimizing thus the whole procedure.     

线形(n,f,k)系统和系统的可靠度计算新方法

本文应用两端同时进行的有限马尔可夫链嵌入法给出了具有复合失效准则的(n,f,k)系统和系统可靠度计算公式及公式中连接矩阵的结构特点。数值计算结果表明,随着构成系统的单元个数的增加,应用两端同时进行的有限马尔可夫链嵌入法比应用传统的有限马尔可夫链嵌入法计算可靠度能节省大量运算时间,特别是对于具有对称结构的(n,f,k)和系统效果更加明显。     

Using genetic algorithm for dynamic and multiple criteria web-site optimizations

In today’s competitive electronic marketplace, companies try to create long-lasting relations with their online customers. Log files and registration forms generate millions of online transactions. Companies use new techniques to “mine” these data and establish optimal online storefronts to maximize their web presence. Several criteria, such as minimization of download time, maximization of web-site visualization and product association level, can be used for the optimization of virtual storefronts. This paper introduces a genetic algorithm, to be used in a model-driven decision-support system for web-site optimizations. The algorithm ensures multiple criteria web-site optimizations, and the genetic search provides dynamic and timely solutions independent of the number of objects to be arranged.     

Limit cycle bifurcations by perturbing piecewise smooth Hamiltonian systems with multiple parameters

This paper is concerned with the problem of limit cycle bifurcation for piecewise smooth near-Hamiltonian systems with multiple parameters. By the first Melnikov function, some novel criteria have been established for the existence of multiple limit cycles. Furthermore, an example is included to validate the obtained results by considering the maximum number of limit cycles for a piecewise quadratic system studied in Llibre and Mereu (2014) [12]. Compared with the result in the above reference, one more limit cycle is found by our method.     

The existence and uniqueness of positive periodic solutions of Nicholson-type delay systems

This paper is concerned with a class of Nicholson blowfly systems with multiple time-varying delays. By applying the method of the Lyapunov functional, some criteria are established for the existence and uniqueness of positive periodic solutions of the system. Moreover, an example is given to illustrate the main results.