A Biobjective Method for Sample Allocation in Stratified Sampling

Emilio Carrizosa, Dolores Romero Morales

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

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.
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.
SprogEngelsk
TidsskriftEuropean Journal of Operational Research
Vol/bind177
Udgave nummer2
Sider1074–1089
ISSN0377-2217
DOI
StatusUdgivet - 2007
Udgivet eksterntJa

Emneord

  • Integer programming
  • Stratified random sampling
  • Sample allocation
  • Biobjective integer program
  • Parametric knapsack problem

Citer dette

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A Biobjective Method for Sample Allocation in Stratified Sampling. / Carrizosa, Emilio; Morales, Dolores Romero.

I: European Journal of Operational Research, Bind 177, Nr. 2, 2007, s. 1074–1089.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

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AU - Morales,Dolores Romero

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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

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