An application of approximate dynamic programming in multi-period multi-product advertising budgeting

<p style='text-indent:20px;'>Advertising has always been considered a key part of marketing strategy and played a prominent role in the success or failure of products. This paper investigates a multi-product and multi-period advertising budget allocation, determining the amount of advertising budget for each product through the time horizon. Imperative factors including life cycle stage, <inline-formula><tex-math id="M1">\begin{document}$ BCG $\end{document}</tex-math></inline-formula> matrix class, competitors' reactions, and budget constraints affect the joint chain of decisions for all products to maximize the total profits. To do so, we define a stochastic sequential resource allocation problem and use an approximate dynamic programming (<inline-formula><tex-math id="M2">\begin{document}$ ADP $\end{document}</tex-math></inline-formula>) algorithm to alleviate the huge size of the problem and multi-dimensional uncertainties of the environment. These uncertainties are the reactions of competitors based on the current status of the market and our decisions, as well as the stochastic effectiveness (rewards) of the taken action. We apply an approximate value iteration (<inline-formula><tex-math id="M3">\begin{document}$ AVI $\end{document}</tex-math></inline-formula>) algorithm on a numerical example and compare the results with four different policies to highlight our managerial contributions. In the end, the validity of our proposed approach is assessed against a genetic algorithm. To do so, we simplify the environment by fixing the competitor's reaction and considering a deterministic environment.</p>

Convergence of equilibrium measures corresponding to finite subgraphs of infinite graphs: New examples

A problem from thermodynamic formalism for countable symbolic Markov chains is considered. It concerns asymptotic behavior of the equilibrium measures corresponding to increasing sequences of finite submatrices of an infinite nonnegative matrix A A when these sequences converge to A A . After reviewing the results obtained up to now, a solution of the problem is given for a new matrix class. The geometric language of loaded graphs is used, instead of the matrix language.

PENGARUH MODEL PEMBELAJARAN KOOPERATIF TIPE TEAMS GAMES TOURNAMENT (TGT) TERHADAP HASIL BELAJAR MATRIKS (Studi Kasus pada Siswa Kelas X-G Program Keahlian RPL SMK Senopati Sedati Sidoarjo)

This research was motivated by the low result of learning mathematics SMK SMK Senopati Sedati Sidoarjo, with formulation of the problem is: is there any influence of cooperative learning model type Teams Games Tournament (TGT) to the learning outcomes matrix class X-G Skills Program RPL SMK Senopati Sedati Sidoarjo?. In accordance with the formulation of the problem, then the purpose of this research is to know is there any influence Cooperative learning model type Teams Games Tournament (TGT) to the learning outcomes matrix class X-G Skills Program RPL SMK Senopati Sedati Sidoarjo. This study is a quasi-experimental design with control grop Nonequivalent design. The study population was all students of class X SMK Senopati Sedati Sidoarjo in Semester II Academic Year 2015/2016 and as samples 59 students are 29 students in grade XG as a class experiment using TGT learning model and 30 graders XF as the control class using conventional methods, Collecting data in this study using a written test. Obtained t > t table (2,757 > 2.00) at the level of 95% which means that H0 rejected and H1 accepted. Thus the test results, we can conclude learning outcomes TGT model is better than the conventional method. In other words, there is the influence of cooperative learning model Teams Games Tournament (TGT) to the learning outcomes matrix class X-G RPL SMK Senopati Sedati Sidoarjo.Keywords : Learning Outcomes, Teams Games Tournament (TGT), Cooperative Learning

A new perspective on paranormed Riesz sequence space of non-absolute type

<p>The current article mainly dwells on introducing Riesz sequence space \(r^{q}(\widetilde{B}_{u}^{p})\) which generalized the prior studies of Candan and Güneş [28], Candan and Kılınç [30] and consists of all sequences whose \(R_{u}^{q}\widetilde{B}\)-transforms are in the space \(\ell(p)\), where \(\widetilde{B}=B(r_{n},s_{n})\) stands for double sequential band matrix \((r_{n})^{\infty}_{n=0}\) and \((s_{n})^{\infty}_{n=0}\) are given convergent sequences of positive real numbers. Some topological properties of the new brand sequence space have been investigated as well as \(\alpha\)- \(\beta\)-and \(\gamma\)-duals. Additionally, we have also constructed the basis of \(r^{q}(\widetilde{B}_{u}^{p})\). Eventually, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.</p>

New type of generalized difference sequence space of non-absolute type and some matrix transformations

In the present paper, we introduce a new difference sequence space rqB(u,p) by using the Riesz mean and the B-difference matrix. We show rqB(u,p) is a complete linear metric space and is linearly isomorphic to the space l(p). We have also computed its ?-, ?- and ?-duals. Furthermore, we have constructed the basis of rqB(u,p) and characterize a matrix class (rqB(u, p), l?).