A biobjective method for sample allocation in stratified sampling

Carrizosa, Emilio and Romero-Morales, Dolores (2007) A biobjective method for sample allocation in stratified sampling. European Journal of Operational Research, 177 (2). pp. 1074-1089.

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The two main and contradicting criteria guiding sampling design are accuracy of estimators and sampling costs. In stratified random sampling, the sample size must be allocated to strata in order to optimize both objectives.
In this note we address, following a biobjective methodology, this allocation problem. A two-phase method is proposed to describe the set of Pareto-optimal solutions of this nonlinear integer biobjective problem. In the first phase, all supported Pareto-optimal solutions are described via a closed formula, which enables quick computation. Moreover, for the common case in which sampling costs are independent of the strata, all Pareto-optimal solutions are shown to be supported. For more general cost structures, the non-supported Pareto-optimal solutions are found by solving a parametric knapsack problem. Bounds on the criteria can also be imposed, directing the search towards implementable sampling plans. Our method provides a deeper insight into the problem than simply solving a scalarized version, whereas the computational burden is reasonable.

Item Type: Article
Keywords: Integer programming; Stratified random sampling; Sample allocation; Biobjective integer program; Parametric knapsack problem; management science
Subject(s): Management science
Date Deposited: 27 Aug 2010 13:36
Last Modified: 09 Mar 2017 16:48
Funders: N/A
URI: http://eureka.sbs.ox.ac.uk/id/eprint/428

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