The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

How to select the optimal supplier is an open and important issue in supply chain management, which can be considered as a multi-criteria decision-making (MCDM) problem. The assessment of experts plays a very important role in the process of supplier selection, while their subjective judgment could produce unpredictable uncertainty. However, existing methods cannot represent and deal with the uncertainty effectively. Dempster–Shafer evidence theory (D–S theory) is widely used in uncertainty modeling, decision-making and conflicts management due to its advantages of handling uncertain information. The VIKOR method has a great advantage to handle MCDM problems with non-commensurable and even conflicting criteria, and to obtain the compromised optimal solution. In this paper, the DS-VIKOR method is proposed for supplier selection problem, which expends the VIKOR method by D–S theory. In the proposed method, the basic probability assignment is used to denote the assessment of domain experts for alternatives, Deng entropy weight-based method is defined and applied to determine the weights of multi-criteria, and VIKOR method is used to get the final ranking results. A numerical example for supplier selection is conducted to analyze and demonstrate the practicality and effectiveness of the proposed DS-VIKOR method.

DS-VIKOR: A New Multi-criteria Decision-Making Method for Supplier Selection

Queueing systems with server vacations (server's performing non-queueing jobs) have been studied extensively since the late 70's. A considerable number of works in this area were completed in the early 80's and surveyed by Doshi in 1986. As an extension to the classical queueing system, allowing idle servers to work on non-queueing jobs makes the vacation models more applicable in a variety of systems including flexible manufacturing or service and computer communication systems. Motivated by these applications, more studies on vacation models have been done during the late 80's and 90's and surveyed in the book by Takagi in 1991 and the book by Tian and Zhang in 2006. This paper intends to provide a brief summary of the most recent research works on vacation queueing systems in the past 10 years. Keywords  server's vacation, batch arrivals, modified vacation policy, working vacations, multi-server vacation models.

http://www.orstw.org.tw/ijor/vol7no4/2-Vol.%207,%20No.4%20pp.3-8.pdf

Recent Developments in Vacation Queueing Models : A Short Survey

C. A. BREBBIA and J. J. CONNOR, The journal will be published quarterly at an annual subscription of £ 25.00 ($ 65.00).

/pdf/applied-mathematical-modelling-4ixr2mcndh.pdf

Applied Mathematical Modelling

Traditionally, the processing times of jobs are assumed to be fixed and known throughout the entire process. However, recent empirical research in several industries has demonstrated that processin...

Scheduling problems under learning effects: classification and cartography

Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns

https://ir.nctu.edu.tw:443/bitstream/11536/15644/1/000300808000028.pdf

Multi-server machine repair model with standbys and synchronous multiple vacation

https://ir.nctu.edu.tw:443/bitstream/11536/5405/1/000276790000018.pdf

Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation

In this paper, we consider the supplier selection problem for normally distributed processes with multiple independent characteristics based on process capability index CpU . A two-phase testing procedure based on the quotient of two statistics is proposed to deal with the problem. We obtain the sampling distribution and the probability density function of the quotient. Several tables of the critical values for the testing procedure and decision making are provided. The required sample sizes for various capability requirements, magnitude of difference of two suppliers, and given power are also presented. A real application on TFT-LCD manufacturing processes is presented to demonstrate the efficacy of the proposed method.

Chia-Huang Wu

Papers

Recent Developments in Vacation Queueing Models : A Short Survey

Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns

Multi-server machine repair model with standbys and synchronous multiple vacation

Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation

Supplier Selection for Multiple-Characteristics Processes with One-Sided Specifications