STOCHASTIC COMPROMISE MIXED ALLOCATION

Clark and Steel [3] worked out the optimum allocation of sample sizes to strata and stages with additional constraints to use different type of allocations in different strata. Ahsan et al. [1] used the same idea to introduced “Mixed Allocation” for univariate stratified populations that maximizes the precision of the estimate of the population mean. Ahsan et al. [2] worked out the Mixed Allocation for fixed precision to minimize the cost of the survey for univariate stratified populations. Later on Varshney and Ahsan [13, 14] extended these works for multivariate stratified populations to obtain a ‘Compromise Mixed Allocation’. This paper, studies a more realistic situation in multivariate stratified sampling. Often the stratum variances are unknown and estimated by their sample estimates that are random variables. The cost of measurement may also vary randomly during the course of sampling. Thus it will be more appropriate to consider the problem of finding a compromise mixed allocation as a Stochastic Nonlinear Programming Problem (SNLPP). The SNLPP is solved using Chance Constrained Technique. The application of this approach is exhibited through a numerical example assuming normal distributions of the random parameters. The numerical results are obtained by using the optimization software LINGO [9]