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

In this paper, we define Einstein product and Einstein sum of fuzzy soft multi sets (FSM-sets) and using these products, we introduce an adjustable approach to FSM-set based decision-making, for solving decision-making in an uncertain situation. The feasibility of our proposed FSM-set based decision-making procedure in practical application is shown by some numerical examples. 


https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/32546/751375153600

Einstein-operations on fuzzy soft multi sets and decision making

In this paper we consider generalized Leontief model 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

A graph $G$ is Hamiltonian-connected if there exists a Hamiltonian path between any two vertices of $G$. It is known that if $G$ is 2-connected then the graph $G^2$ is Hamiltonian-connected. In this paper we prove that the square of every self-complementary graph of order grater than 4 is Hamiltonian-connected. If $G$ is a $k$-critical graph, then we prove that the Mycielski graph $\mu(G)$ is $(k+1)$-critical graph. Jarnicki et al.[7] proved that for every Hamiltonian graph of odd order, the Mycielski graph $\mu(G)$ of $G$ is Hamiltonian-connected. They also pose a conjecture that if $G$ is Hamiltonian-connected and not $K_2$ then $\mu(G)$ is Hamiltonian-connected. In this paper we also prove this conjecture.

On Hamiltonian-Connected and Mycielski graphs

In this paper, we revisit Scarf’s generalization of the linear complementarity problem, formulate this as a vertical linear complementarity problem and obtain some new results on this generalization. Also, a neural network model for solving Scarf’s generalized complementarity problems is proposed. Numerical simulation results show that the proposed model is feasible and efficient. Keywords: Scarf’s complementarity problem, Vertical linear complementarity problem, Cottle-Dantzig’s algorithm, Lemke’s algorithm, Neural network approach. MSC : 90C33, 92B20

/pdf/scarf-s-generalization-of-linear-complementarity-problem-3ja4gj21hu.pdf

Scarf’s generalization of linear complementarity problem revisited

A class of graphs $\mathcal{C}$ is closed under powers if for every graph $G\in\mathcal{C}$ and every $k\in\mathbb{N}$, $G^k\in\mathcal{C}$. Also $\mathcal{C}$ is strongly closed under powers if for every $k\in\mathbb{N}$, if $G^k\in\mathcal{C}$, then $G^{k+1}\in\mathcal{C}$. It is known that circular arc graphs and proper circular arc graphs are closed under powers. But it is open whether these classes of graphs are also strongly closed under powers. In this paper we have settled these problems.

A. K. Das

Papers

Einstein-operations on fuzzy soft multi sets and decision making

Iterative Descent Method for Generalized Leontief Model

On Hamiltonian-Connected and Mycielski graphs

Scarf’s generalization of linear complementarity problem revisited

On powers of circular arc graphs