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

More on positive subdefinite matrices and the linear complementarity problem

On the classes of fully copositive and fully semimonotone matrices

Mathematical Programming and Its Applications in Finance Linear Programs with Totally Unimodular Coefficient Matrix Interior Point Method for Convex Quadratic Programming Analysis of Sets of Constraints, Traveling Salesman Problem and Tolerance-Based Algorithms Pedigree Polytope One-Defective Vertex Coloring Problem Complementarity Problem Fuzzy Twin Support Vector Machines for Pattern Classification Minimum Sum of Absolute Errors Regression Hedging Against the Market with No Short Selling Mathematical Programming and Electrical Network Analysis Dynamic Optimal Control Policy Forecasting for Supply Chain and Portfolio Management Variational Analysis in Bilevel Programming Game Engineering Games of Connectivity Robust Feedback Nash Equilibrium De Facto Delegation and Proposer Rules Bargaining Set in Effectivity Function Dynamic Oligopoly as a Mixed Large Game -- Toy Market, Balanced Games, Market Equilibrium for Combinatorial Auctions and the Matching Core of Non-negative TU Games Continuity, Manifolds and Arrow's Social Choice Problem Mixture Class of Stochastic Games.

/pdf/mathematical-programming-and-game-theory-for-decision-making-jmfndi2ynp.pdf

Mathematical programming and game theory for decision making

In this paper we consider criss-cross method for finding solution of a linear complementarity problem. The criss-cross method is a pivoting procedure. We show that the criss-cross method is able to compute solution of a linear complementarity problem in finite steps in case of some new matrix classes. We present a numerical illustration to show a comparison between criss-cross method and Lemke’s algorithm with respect to number of iterations before finding a solution. Finally we raise an open problem in the context of criss-cross method.

Finiteness of Criss-Cross Method in Complementarity Problem

In this article, we introduce a new matrix class almost (a subclass of almost N 0-matrices which are obtained as a limit of a sequence of almost N-matrices) and obtain a sufficient condition for this class to hold Q-property. We produce a counter example to show that an almost -matrix need not be a R 0-matrix. We also introduce another two new limiting matrix classes, namely of exact order 2, for a positive vector d and prove sufficient conditions for these classes to satisfy Q-property. Murthy et al. [Murthy, G.S.R., Parthasarathy, T. and Ravindran, G., 1993, A copositive Q-matrix which is not R 0. Mathematical Programming, 61, 131–135.] showed that Pang's conjecture ( ) is not true even when E 0 is replaced by C 0. We show that Pang's conjecture is true if E 0 is replaced by almost C 0 Finally, we present a game theoretic proof of necessary and sufficient conditions of an almost P 0-matrix satisfying Q-property.

A. K. Das

Papers

More on positive subdefinite matrices and the linear complementarity problem

On the classes of fully copositive and fully semimonotone matrices

Mathematical programming and game theory for decision making

Finiteness of Criss-Cross Method in Complementarity Problem

On almost type classes of matrices with Q-property