Stochastic Programming Approach in Stratified Sampling Problems

This book is based on the application of Stochastic programming techniques in Stratified Sampling problems. Stochastic programming deals with a class of optimization models and algorithms in which some of the data may be considered as random. First chapter provides a brief historical sketch of mathematical programming, stochastic programming and its application to various fields including sampling are presented. Various methods namely E-model, modified E-model, Branch and Bound approach and chance constrained programming are used to solve Probabilistic objective function & constraint into an equivalent deterministic. Allocation problems arising in univariate sratified sampling have been considered in first four (II-V) chapters and multivariate case in the last chapter. The problems are solved by first deriving the deterministic equivalents and then by using a suitable convex programming algorithm or by using the Chance constrained technique. Allocation problem in two stage stratified sampling with random parameters in both objective and constraints is also discussed. A numerical example is presented in all chapters and the problems are solved by LINGO software.