Product line selection and pricing analysis: Impact of genetic relaxations

A model for the product line selection and pricing problem (PLSP) is presented andthree solution procedures based on a genetic algorithm are developed to analyze the results based on consumer preference patterns. Since the PLSP model is nonlinear and integer, two of the solution procedures use genetic encoding to “relax” the NP hard model. The relaxations result in linear integer and shortest path models for the fitness evaluation which are solved using branch and bound and labeling algorithms, respectively. Performance of the quality of solutions generated by the procedures is evaluated for various problem sizes and customer preference structures. The results show that the genetic relaxations provide efficient and effective solution methodologies for the problem, when compared to the pure artificial intelligence technique of genetic search. The impact of the preference structure on the product line and the managerial implications of the solution characteristics generated by the genetic relaxations are also discussed. The models can be used to explicitly consider tradeoffs between marketing and operations concerns in designing a product line.     

Dependence properties and comparison results for Lévy processes

In this paper we investigate dependence properties and comparison results for multidimensional Lévy processes. In particular we address the questions, whether or not dependence properties and orderings of the copulas of the distributions of a Lévy process can be characterized by corresponding properties of the Lévy copula, a concept which has been introduced recently in Cont and Tankov (Financial modelling with jump processes. Chapman & Hall/CRC, Boca Raton, 2004) and Kallsen and Tankov (J Multivariate Anal 97:1551–1572, 2006). It turns out that association, positive orthant dependence and positive supermodular dependence of Lévy processes can be characterized in terms of the Lévy measure as well as in terms of the Lévy copula. As far as comparisons of Lévy processes are concerned we consider the supermodular and the concordance order and characterize them by orders of the Lévy measures and by orders of the Lévy copulas, respectively. An example is given that the Lévy copula does not determine dependence concepts like multivariate total positivity of order 2 or conditionally increasing in sequence. Besides these general results we specialize our findings for subfamilies of Lévy processes. The last section contains some applications in finance and insurance like comparison statements for ruin times, ruin probabilities and option prices which extends the current literature. Anja Blatter was supported by the Deutsche Forschungsgemeinschaft (DFG).     

Necessary and Sufficient Conditions for the Boundedness of the Riesz Potential in Local Morrey-type Spaces

The problem of the boundedness of the Riesz potential I _α , 0 < α < n, in local Morrey-type spaces is reduced to the boundedness of the Hardy operator in weighted L _p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for the boundedness in local Morrey-type spaces for all admissible values of the parameters. Moreover, for a certain range of the parameters, these sufficient conditions coincide with the necessary ones. V. Guliyev’s research was partially supported by the grant of the Azerbaijan-U. S. Bilateral Grants Program II (project ANSF Award / AZM1-3110-BA-08) and the Turkish Scientific and Technological Research Council (TUBITAK, programme 2221, no. 220.01-619-4889).     

Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

Parameter estimation for stochastic equations with additive fractional Brownian sheet

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory.      

Chaos control of a fractional order modified coupled dynamos system

This paper analyzes some Routh-Hurwitz stability conditions generalized to the fractional order case, and discusses the stability region of the fractional order system. We analyze the chaotic behavior of the fractional order modified coupled dynamos system concretely, and provide the conditions suppressing chaos to unstable equilibrium points, then use the feedback control method to control chaos in the fractional order modified coupled dynamos system. Numerical simulations show the effectiveness of the method.     

Order selection and pricing methods using flexible quantity and fuzzy approach for buyer evaluation

This paper presents the methods for order selection and pricing of manufacturer (supplier) with make-to-order basis when orders exceed production capacity. By quoting the concepts of triangular fuzzy numbers and linguistic variables, a fuzzy approach to evaluating buyers by taking into account both positive and negative criteria is proposed. According to the classified results of buyers, the orders will be produced with priority, declined, or determined by MIP model. The fixed quantity MIP model and flexible quantity MIP model are employed to determine the produced orders along with the production quantity and the reference amount for price reduction. By applying the concept of TOPSIS, the closeness coefficients for satisfaction grades of orders and for ranking values of buyers are used as the adjusting rates in the final pricing MIP model to set segmented price.     

Numerical methods for nonlinear partial differential equations of fractional order

In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when applied to partial differential equations of fractional order.     

On the stability of jump-diffusions with Markovian switching

In this paper we consider the stability for a class of jump-diffusions with Markovian switching. We first construct them successively and show that they can be associated with some appropriate generators and they are non-explosive. We then prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity by making use of the relation between the transition probabilities of jump-diffusions and the corresponding diffusions. Finally, we also investigate their exponential ergodicity.     

On a fractional integral equation of periodic functions involving Weyl-Riesz operator in Banach algebras

In this paper, we study the existence of periodic solutions for a nonlinear integral equation of periodic functions involving Weyl-Riesz fractional integral operator under the mixed generalized Lipschitz, Carathéodory and monotonicity conditions. The fixed point theorems due to Dhage are the main tool in carrying out our proofs.