Integer optimization in sample surveys

Abstract

The present thesis entitled Integer Optimization in Sample Surveys is an outcome of the studies made by the author at the Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India. newlineThere are two generally accepted options for studying the characteristics of a finite population. The first is to study each and every unit of the population. This is called census or complete enumeration. The other is through the study of only a selected portion of the population. This selected portion is called a sample and this method is called sampling or sample survey. Census is time consuming, expensive, even impossible in some situations and often in accurate. On the other hand a sample survey costs less in terms of time and money both and usually is more accurate then census. A good survey free from errors and biases can render a very useful service in the solution of many socio-economic problems of a country by accelerating the timely flow of adequate and reliable information. Mathematical programming is concerned with the determination of the minimum or maximum of a function of several variables, which are subject to a number of constraints. Such situations exist in diverse fields of human activities e. g. Engineering Sciences, Operations Research, Management Sciences, Computer Sciences, Numerical analysis, System analysis, Economics, Military Sciences, Transportations, Assignments, Medical Sciences, Agriculture, Statistical analysis etc. This thesis is an attempt to formulate some problems arising in univariate and multivariate stratified sample surveys as mathematical programming problems and various techniques are developed for their solution. The thesis consists of seven chapters. Articles, definitions and equations have been numbered chapter wise in such a way that, when read as decimals they stand in their proper order e.g., (6.5.1) refers to equation number 1 of section 5 of chapter 6.