A. K. Das

Bio: A. K. Das is an academic researcher from Indian Statistical Institute. The author has contributed to research in topics: Linear complementarity problem & Complementarity theory. The author has an hindex of 8, co-authored 41 publications receiving 180 citations.

Application of Multivariate Analysis to Increase the Yield of Dry Cell Batteries

Abstract: In an organization, the manufacturing process of a dry cell battery was suffering from the problem of frequent stoppages in the assembly line The complete battery manufacturing operation is highly automated and mechanized It was suspected that excessive variation in overall height of bobbin was the major reason for such stoppages The bobbin, the inside part of a dry cell battery acting as cathode, is formed by the battery extrusion process A planned experiment was carried out on the extrusion process that identified the setting of extrusion machines and the amount of water content in the cathode mixture as the parameters causing variation in the bobbin characteristics The problem of frequent stoppages was eliminated when appropriate action was taken on these two parameters Finally, multivariate and univariate control schemes were developed for online control of the bobbin characteristics

Generalized Monotone Maps and Complementarity Problems

Abstract: In this chapter, we present some classes of generalized monotone maps and their relationship with the corresponding concepts of generalized convexity. We present results of generalized monotone maps that are used in the analysis and solution of variational inequality and complementarity problems. In addition, we obtain various characterizations and establish a connection between affine pseudomonotone mapping, affine quasimonotone mapping, positive-subdefinite matrices, generalized positive-subdefinite matrices, and the linear complementarity problem. These characterizations are useful for extending the applicability of Lemke’s algorithm for solving the linear complementarity problem.

Artificial Neural Network Model for Forecasting the Stock Price of Indian IT Company

Abstract: The central issue of the study is to model the movement of stock price for Indian Information Technology (IT) companies. It has been observed that IT industry has some promising role in Indian economy. We apply the artificial neural networks (ANNs) for modeling purpose. ANNs are flexible computing frameworks and its universal approximations applied to a wide range with desired accuracy. In the study, multilayer perceptron (MLP) models, which are basically feed-forward artificial neural network models, are used for forecasting the stock values of an Indian IT company. On the basis of various features of the network models, an optimal model is being proposed for the purpose of forecasting. Performance measures like \(\text {R}^{2}\), standard error of estimates, mean absolute error, mean absolute percentage error indicate that the model is adequate with respect to acceptable accuracy.

Forecasting models for developing control scheme to improve furnace run length

Abstract: In petrochemical industries, the gaseous feedstock like ethane and propane are cracked in furnaces to produce ethylene and propylene as main products and the inputs for the other plant in the downstream. A problem of low furnace run length (FRL) increases furnace decoking and reduces productivity along with the problem of reducing life of the coil. Coil pressure ratio (CPR) and tube metal temperature (TMT) are the two most important performance measures for the FRL to decide upon the need for furnace decoking. This article, therefore, makes an attempt to develop the prediction models for CPR and TMT based on the critical process parameters, which would lead to take the necessary control measures along with a prior indication for decoking. Regression-based time series and double exponential smoothing techniques are used to build up the models. The effective operating ranges of the critical process parameters are found using a simulation-based approach. The models are expected to be the guiding principles e...

On Column Competent Matrices and Linear Complementarity Problem

Abstract: We revisit the class of column competent matrices and study some matrix theoretic properties of this class. The local $w$-uniqueness of the solutions to the linear complementarity problem can be identified by the column competent matrices. We establish some new results on $w$-uniqueness properties in connection with column competent matrices. These results are significant in the context of matrix theory as well as algorithms in operations research. We prove some results in connection with locally $w$-uniqueness property of column competent matrices. Finally we establish a connection between column competent matrices and column adequate matrices with the help of degree theory.

The Design and Analysis of Experiments

Abstract: 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

Applications in Statistics to Industrial Experimentation.

Abstract: 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.

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

Abstract: 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 Twin Multi-Class Classification Support Vector Machine

Abstract: 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.