A Biobjective Method for Sample Allocation in Stratified Sampling

Emilio Carrizosa, Dolores Romero Morales

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

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.
Original languageEnglish
JournalEuropean Journal of Operational Research
Volume177
Issue number2
Pages (from-to)1074–1089
ISSN0377-2217
DOIs
Publication statusPublished - 2007
Externally publishedYes

Cite this

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title = "A Biobjective Method for Sample Allocation in Stratified Sampling",
abstract = "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.",
keywords = "Integer programming, Stratified random sampling, Sample allocation, Biobjective integer program, Parametric knapsack problem",
author = "Emilio Carrizosa and {Romero Morales}, Dolores",
year = "2007",
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pages = "1074–1089",
journal = "European Journal of Operational Research",
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A Biobjective Method for Sample Allocation in Stratified Sampling. / Carrizosa, Emilio; Romero Morales, Dolores .

In: European Journal of Operational Research, Vol. 177, No. 2, 2007, p. 1074–1089.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - A Biobjective Method for Sample Allocation in Stratified Sampling

AU - Carrizosa, Emilio

AU - Romero Morales, Dolores

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Integer programming

KW - Stratified random sampling

KW - Sample allocation

KW - Biobjective integer program

KW - Parametric knapsack problem

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DO - 10.1016/j.ejor.2005.11.027

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VL - 177

SP - 1074

EP - 1089

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

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ER -