Competitive strategies and market segmentation for suppliers with substitutable products

This research studies the competition between two coexisting suppliers in a two-echelon supply chain. The suppliers have different inventory cost structures (holding cost and setup cost). Each supplier offers one type of the two substitutable products to multiple buyers. Buyers’ preferences between the substitutable products differ. Each buyer has a particular order profile (order frequency and quantity). A buyer chooses between the suppliers based on the prices offered by both suppliers and his/her own preference. A Hotelling-type model is used to describe buyers’ preferences for the products. We are able to describe the conditions for buyers to switch between the suppliers, and therefore spot the buyer groups that may or may not switch when the suppliers compete. Pricing strategies for different buyer groups are suggested to the competitive suppliers accordingly. Furthermore, equilibrium prices, market segments, and overall profits for the suppliers are revealed based on Game Theory. An algorithm is also proposed to forecast buyers’ reactions to suppliers’ pricing strategies given the buyers’ order profiles and preferences between the substitutable products.     

Lower complexity bounds for interpolation algorithms

We introduce and discuss a new computational model for the Hermite-Lagrange interpolation with nonlinear classes of polynomial interpolants. We distinguish between an interpolation problem and an algorithm that solves it. Our model includes also coalescence phenomena and captures a large variety of known Hermite-Lagrange interpolation problems and algorithms. Like in traditional Hermite-Lagrange interpolation, our model is based on the execution of arithmetic operations (including divisions) in the field where the data (nodes and values) are interpreted and arithmetic operations are counted at unit cost. This leads us to a new view of rational functions and maps defined on arbitrary constructible subsets of complex affine spaces. For this purpose we have to develop new tools in algebraic geometry which themselves are mainly based on Zariski’s Main Theorem and the theory of places (or equivalently: valuations). We finish this paper by exhibiting two examples of Lagrange interpolation problems with nonlinear classes of interpolants, which do not admit efficient interpolation algorithms (one of these interpolation problems requires even an exponential quantity of arithmetic operations in terms of the number of the given nodes in order to represent some of the interpolants).In other words, classic Lagrange interpolation algorithms are asymptotically optimal for the solution of these selected interpolation problems and nothing is gained by allowing interpolation algorithms and classes of interpolants to be nonlinear. We show also that classic Lagrange interpolation algorithms are almost optimal for generic nodes and values. This generic data cannot be substantially compressed by using nonlinear techniques.We finish this paper highlighting the close connection of our complexity results in Hermite-Lagrange interpolation with a modern trend in software engineering: architecture tradeoff analysis methods (ATAM).     

Fuzzy analytic hierarchy process: A logarithmic fuzzy preference programming methodology

Fuzzy analytic hierarchy process (AHP) proves to be a very useful methodology for multiple criteria decision-making in fuzzy environments, which has found substantial applications in recent years. The vast majority of the applications use a crisp point estimate method such as the extent analysis or the fuzzy preference programming (FPP) based nonlinear method for fuzzy AHP priority derivation. The extent analysis has been revealed to be invalid and the weights derived by this method do not represent the relative importance of decision criteria or alternatives. The FPP-based nonlinear priority method also turns out to be subject to significant drawbacks, one of which is that it may produce multiple, even conflict priority vectors for a fuzzy pairwise comparison matrix, leading to entirely different conclusions. To address these drawbacks and provide a valid yet practical priority method for fuzzy AHP, this paper proposes a logarithmic fuzzy preference programming (LFPP) based methodology for fuzzy AHP priority derivation, which formulates the priorities of a fuzzy pairwise comparison matrix as a logarithmic nonlinear programming and derives crisp priorities from fuzzy pairwise comparison matrices. Numerical examples are tested to show the advantages of the proposed methodology and its potential applications in fuzzy AHP decision-making.     

一类非最小相位非线性系统的鲁棒输出调节

研究了一类具有非最小相位和非线性外部系统的非线性系统的全局鲁棒输出调节问题.首先,利用浸入系统设计了一个非线性内模.其次,把原系统的全局鲁棒输出调节问题转化为增广系统的全局鲁棒镇定问题.然后,利用改变能量函数和动态增益技巧设计了一个状态反馈控制器,使得闭环系统的解有界并且跟踪误差渐近趋于零.最后,利用仿真结果验证了所设计的控制器的有效性.     

分布时滞系统的动态输出反馈鲁棒稳定

主要研究了一类具分布时变时滞不确定系统的输出反馈鲁棒稳定问题.基于动态输出反馈和Lyapunov-Krasovskii泛函,给出了闭环系统与时滞相关的鲁棒稳定的条件.所得条件为线性矩阵不等式形式,便于运用内点算法进行求解.     

基于灰色聚类的多指标稳健性设计研究

随着市场竞争的日趋激烈,迫切地需要将产品的质量、成本、效益和顾客的满意度等市场竞争要素一起综合考虑进行稳健性设计.采用灰色聚类多指标综合评价对定性、定量指标用灰数的白化权函数加以聚类,对试验方案进行初步筛选,然后在备选方案中对同属于"优"类别的方案进行综合分析,得到一组最佳可控因子组合,并进行验证性分析.最后利用此方法对一款洗衣机用串激电机从成本、效益和顾客满意度方面综合进行考虑,进行了稳健性设计,得到真正意义上的低成本、高质量、高可靠性和高效益的产品,从而最终为解决这种带有模糊性因素的多指标优化问题开创了一种稳健性设计新思路.     

均值方差结构模型的渐近稳健推断(英文)

均值方差模型广泛应用于行为、教育、医学、社会和心理学的研究.经典的极大似然估计对于异常点和分布扰动易受影响.本文基于目标函数最小化给出稳健估计,并基于稳健偏差提出模型拟合.     

不连续全局优化问题的对数变差积分途径

针对不连续无约束全局优化问题,构造且运用对数变差积分来进行研究和求解.具体给出了对数变差积分函数的分析性质及其全局优化问题的最优性条件和概念性算法.结合Monte-Carlo技术,特别针对n=100个变量、具有不连续目标函数的三个具体实例进行了数值试验,计算结果也表明所给方法的可行性和有效性.     

Soliton solution to the complex modified Korteweg–de Vries equation on both zero and nonzero background via the robust inverse scattering method

In this paper, based on the robust inverse scattering method, we construct two kinds of solutions to the focusing modified Korteweg–de Vries equation. One is the classical soliton solution under the zero background condition and the other one is given through the nonzero background. Especially, for the nonzero background case, we choose a special spectral parameter such that the nonzero background solution is changed into the rational travelling waves. Finally, we also give a simple analysis of the soliton as the time $t$ is large, then we give the comparison between the exact solution and the asymptotic solution.     

Enhanced interactive satisficing method via alternative tolerance for fuzzy goal programming with progressive preference

This paper proposes an enhanced interactive satisficing method via alternative tolerance for fuzzy goal programming with progressive preference. The alternative tolerances of the fuzzy objectives with three types of fuzzy relations are used to model progressive preference of decision maker. In order to improve the dissatisficing objectives, the relaxed satisficing objectives are sacrificed by modifying their tolerant limits. By means of attainable reference point, the auxiliary programming is designed to generate the tolerances of the dissatisficing objectives for ensuring feasibility. Correspondingly, the membership functions are updated or the objective constraints are added. The Max–Min goal programming model (or the revised one) and the test model of the M-Pareto optimality are solved lexicographically. By our method, the dissatisficing objectives are improved iteratively till the preferred result is acquired. Illustrative examples show its power.