A combinatorial optimization approach to the selection of statistical units

Renato  Bruni; Gianpiero  Bianchi; Alessandra  Reale

doi:10.3934/jimo.2016.12.515

Article Contents

2016, Volume 12, Issue 2: 515-527. Doi: 10.3934/jimo.2016.12.515

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A combinatorial optimization approach to the selection of statistical units

1.
Università di Roma "Sapienza", Dip. di Ing. Informatica, Automatica e Gestionale (DIAG), Via Ariosto 25, Roma, 00185
2.
Italian National Statistic Office “Istat", Dip. per i Censimenti e gli Archivi Amm. e Statistici (DICA), Viale Oceano Pacifico 171, Roma, 00144
3.
Italian National Statistic Office “Istat”, Dip. per i Censimenti e gli Archivi Amm. e Statistici (DICA), Viale Oceano Pacifico 171, Roma, 00144

Received: March 31, 2014

Revised: October 31, 2014

Published: March 2016

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Abstract

In the case of some large statistical surveys, the set of units that will constitute the scope of the survey must be selected. We focus on the real case of a Census of Agriculture, where the units are farms. Surveying each unit has a cost and brings a different portion of the whole information. In this case, one wants to determine a subset of units producing the minimum total cost for being surveyed and representing at least a certain portion of the total information. Uncertainty aspects also occur, because the portion of information corresponding to each unit is not perfectly known before surveying it. The proposed approach is based on combinatorial optimization, and the arising decision problems are modeled as multidimensional binary knapsack problems. Experimental results show the effectiveness of the proposed approach.

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Mathematics Subject Classification: Primary: 90C90, 90C06; Secondary: 05A99.

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