


  Programming (Mathematics) 

  Use of mathematical programming in stratification with cost constraint Author: Fonolahi, Aluwesi Volau Institution: University of the South Pacific. Award: M.Sc. Subject: Programming (Mathematics) Date: 2015 Call No.: Pac QA 402 .5 .F66 2015 BRN: 1204056 Copyright:Under 10% of this thesis may be copied without the authors written permission Abstract: The aim of survey design is to obtain maximum precision at minimum cost. To achieve this, stratified random sampling is one of the commonly used sampling techniques in designing a survey. While using stratified sampling, the problem of stratification, that is, determining optimum strata boundaries (OSB) is one of the main problems encountered by survey designers. Many authors have proposed different methods of determining the OSB by considering merely a fact that the total sample size is fixed. They ignored the fact that the cost of measurement per unit may vary from stratum to stratum. This research is an attempt to determine the OSB when the budget of the targeted survey is fixed in advance and the measurement cost per unit varies across the strata. The problem is formulated as a mathematical programming problem and solved to obtain the optimum strata width, which is then used to calculate the optimum strata boundaries. The formulated mathematical programming problem, being a multistage problem is solved by developing a Dynamic Programming Technique. Numerical examples using the population in which the stratification variables follow the exponential distribution, righttriangular distribution, Cauchy distribution and the power distribution are presented to illustrate the procedure developed in this thesis.


