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The multi-quadrics (MQ) function is a kind of radial basis function. And the MQ method has been successfully adopted as a type of meshless method in solving electromagnetic boundary value problems. However, the accuracy of MQ interpolation or solving equations is severely influenced by shape parameter. Thus the purpose of this paper is to propose a case-independent shape parameter selection strategy from the aspect of coefficient matrix condition number analysis.

The condition number of coefficient matrix is investigated. It is shown that the condition number is only a function of shape parameter and MQ node number, and is irrelevant to the interpolated function which means case-independent. The effective condition number which takes into account the interpolated function is introduced. Then, the relation between the relative root mean square error and condition number is analyzed. Three numerical experiments as transmission line, cable channel and grounding metal box model were carried out.

In the numerical experiments, there is an approximate linear relationship between the logarithm of the condition number and shape parameter, an approximate quadratic relationship with node number. And the optimal shape parameter is corresponding to the early stage of condition number oscillation.

This paper proposed a case-independent shape parameter selection strategy. For a finite precision computation, the upper limit of the condition number is predetermined. Therefore, the shape parameter can be chosen where condition number oscillates in early stage.

The purpose of this paper is to solve the interface discontinuities in radial basis function (RBF) method for multi-medium boundary value problems (BVPs). The discontinuity of the solution derivatives is not easily handled with RBF method because of infinitely smoothness.

The essence of solving BVP is to construct the continuous potential function surfaces. Hence, from constructing surface aspect, this paper proposed and compared the global and subzone schemes for RBF method. Their implementation schemes and mathematic models can then be derived. Numerical experiments and comparison are carried out for electric and magnetic field calculation.

In the numerical experiments, the subzone scheme has shown its significant advantageous, it can approximate not only the potential function but also its derivative on interface boundary with high accuracy. So the physical characteristics of discontinuities on the interface can be revealed clearly. The overall precision is significantly improved.

This paper proposed an effective subzone scheme for RBF method in multi-medium BVP. It is an improvement for RBF method based on its domain decomposition idea. And it is also a candidate for solving complex BVP.

The purpose of this paper is to propose a forecasting model to predict the demand under uncertain environment to control the bullwhip effect (BWE) considering review-period order-up-to level ((R, S)) inventory control policy and its different variants such as (R, βS) (R, γO) and (R, γO, βS) proposed by Jakšič and Rusjan, (2008) and Bandyopadhyay and Bhattacharya (2013).

A hybrid forecasting model has been developed by combining the feature of discrete wavelet transformation (DWT) and an intelligence technique, multi-gene genetic programming (MGGP), denoted as DWT-MGGP. Performance of DWT-MGGP model has been verified under (R, S) inventory control policy considering demand from three different manufacturing companies.

A comparison between DWT-MGGP model and autoregressive integrated moving average forecasting model has been done by estimating forecast error and BWE. Further, this study has been extended with analysing the behaviour of BWE considering different variants of (R, S) policy such as (R,βS) (R, γO) and (R,γO,βS) and found that BWE can be moderated by controlling the inventory smoothing (β) and order smoothing parameters (γ).

This study is limited to different variants of (R, S) inventory control policy. However, this study can be further extended to continuous review policy.

The proposed DWT-MGGP model can be used as a suitable demand forecasting model to control the BWE when (R, S), (R,βS) (R,γO) and (R,γO,βS)inventory control policies are followed for replenishment.

This study analyses the behavior of BWE through controlling the inventory smoothing (β) and order smoothing parameters (γ) when demand is predicted using DWT-MGGP forecasting model and order is estimated using (R, S), (R,βS) (R,γO) and (R,γO,βS) inventory control policies.