Determining the Optimum Stratum Boundaries Using Mathematical Programming

摘要

The method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation, is known as optimum stratification. Inorder to make the strata internally homogeneous, the strata are constructed in sucha way that the strata variances should be as small as possible for the characteristicunder study. In this paper the problem of determining optimum strata boundaries(OSB) is discussed when strata are formed based on a single auxiliary variable with avarying measurement cost per units across strata. The auxiliary variable consideredin the problem is a size variable that holds a common model for a whole population.The OSB are achieved effectively by assuming a suitable distribution of the auxiliaryvariable and creating strata by cutting the range of the distribution at optimumpoints. The problem of finding the OSB, which minimizes the variance of the esti-mated population mean under a weighted stratified balanced sampling, is formulatedas a mathematical programming problem (MPP). Treating the formulated MPP asa multistage decision problem, a solution procedure using dynamic programming technique is developed. A numerical example using a hospital population datais presented to illustrate the computational details of the solution procedure. Asoftware program coded in JAVA is written to carry out the computation. Thedistribution of the auxiliary variable in this example is considered to be continuouswith an exponential density function.