THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

https://bura.brunel.ac.uk/bitstream/2438/17829/4/FullText.pdf

Big data analytics in supply chain management: A state-of-the-art literature review

Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.

Applications in Statistics to Industrial Experimentation.

We address a vendor-managed inventory-routing problem where a supplier (vendor) receives a given amount of a single product each period and distributes it to multiple retailers over a finite time horizon using a capacitated vehicle. Each retailer faces external dynamic demand and is controlled by a deterministic order-up-to level policy requiring that the supplier raise the retailer's inventory level to a predetermined maximum in each replenishment. The problem is deciding on when and in what sequence to visit the retailers such that systemwide inventory holding and routing costs are minimized. We propose a branch-and-cut algorithm and a heuristic based on an a priori tour using a strong formulation. To the best of our knowledge, this study is the first to consider a strong formulation for the inventory replenishment part of inventory-routing problems. Computational results reveal that the new branch-and-cut algorithm and heuristic perform better than those noted in the literature.

A Branch-and-Cut Algorithm Using a Strong Formulation and an A Priori Tour-Based Heuristic for an Inventory-Routing Problem

Twin support vector machine (TSVM) is a novel machine learning algorithm, which aims at finding two nonparallel planes for each class. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems rather than a single large one. Classical TSVM is proposed for the binary classification problem. However, multi-class classification problem is often met in our real world. For this problem, a new multi-class classification algorithm, called Twin-KSVC, is proposed in this paper. It takes the advantages of both TSVM and K-SVCR (support vector classification-regression machine for k-class classification) and evaluates all the training points into a “1-versus-1-versus-rest” structure, so it generates ternary outputs { −1, 0, +1}. As all the samples are utilized in constructing the classification hyper-plane, our proposed algorithm yields higher classification accuracy in comparison with other two algorithms. Experimental results on eleven benchmark datasets demonstrate the feasibility and validity of our proposed algorithm.

A Twin Multi-Class Classification Support Vector Machine

Invex programming problems with equality and inequality constraints

In this article, we show that under certain condition the generalized Leontief model is solvable by iterative descent method based on infeasible interior point algorithm. We prove the convergence of the method from strictly positive starting point. A numerical example is presented to demonstrate the performance of the algorithm.

Iterative Descent Method for Generalized Leontief Model

In this article, we introduce the class of semimonotone star ($E_0^s$) matrices. We establish the importance of the class of $E_0^s$-matrices in the context of complementarity theory. We show that the principal pivot transform of $E_0^s$-matrix is not necessarily $E_0^s$ in general. However, we prove that $\tilde{E_0^s}$-matrices, a subclass of the $E_0^s$-matrices with some additional conditions, is in $E_0^f$ by showing this class is in $P_0.$ We prove that LCP$(q, A)$ can be processable by Lemke's algorithm if $A\in \tilde{E_0^s}\cap P_0.$ We find some conditions for which the solution set of LCP$(q, A)$ is bounded and stable under the $\tilde{E^s_0}$-property. We propose an algorithm based on an interior point method to solve LCP$(q, A)$ given $A \in \tilde{E^{s}_{0}}.$

On Semimonotone Star Matrices and Linear Complementarity Problem

In this paper, we study the existence, uniqueness, and iterative approximations of solutions for the functional equations arising in dynamic programming under Banach spaces and complete metric spaces. Our results unify the results of Bellman [1], Bhakta and Mitra [3], Bhakta and Choudhury [4], Liu [8], Liu and Ume [10], Liu et al. [11], Liu et al. [13], Liu and Kang [9], and Jiang et al. [7]. Examples are provided to support our results.

On Solvability for Certain Functional Equations Arising in Dynamic Programming

This study illustrates how a system of statistical process control consisting of appropriate statistical techniques is introduced in an Indian organization that manufactures ductile iron pipes, with a view to expanding the market for export promotion. This is a part of corporate business strategy of the organization. The statistical system is introduced by taking into account certain critical-to-quality product characteristics of some processes, which have been identified by the auditors of the Korean Standards Association (KSA). The specific recommendations with regard to the introduction of the statistical system are based on an extensive assessment of the existing performance of the identified processes by the authors. Successful implementation of the recommendations enabled the Indian organization to export to Korea in a big way.

A. K. Das

Papers

Invex programming problems with equality and inequality constraints

Iterative Descent Method for Generalized Leontief Model

On Semimonotone Star Matrices and Linear Complementarity Problem

On Solvability for Certain Functional Equations Arising in Dynamic Programming

Introduction of statistical process control system in a ductile iron pipe manufacturing plant for export promotion