Skip to main content
SpringerLink
Log in

Balancing of agricultural census data by using discrete optimization

  • Short Communication
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

In the case of large-scale surveys, such as a Census, data may contain errors or missing values. An automatic error correction procedure is therefore needed. We focus on the problem of restoring the consistency of agricultural data concerning cultivation areas and number of livestock, and we propose here an approach to this balancing problem based on optimization. Possible alternative models, either linear, quadratic or mixed integer, are presented. The mixed integer linear one has been preferred and used for the treatment of possibly unbalanced data records. Results on real-world Agricultural Census data show the effectiveness of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bacharach, M.: Matrix rounding problems. Manag. Sci. 12(9), 732–742 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bacharach, M.: Biproportional Matrices and Input–Output Change. Cambridge University Press, Cambridge (1970)

    MATH  Google Scholar 

  3. Banff Support Team: Functional Description of the Banff System for Edit and Imputation System. Quality Assurance and Generalized Systems Section Technical Reportt Statistics, Canada (2003)

  4. Bankier, M.: Canadian Census Minimum change Donor imputation methodology. In: Proceedings of the Workshop on Data Editing. UN/ECE, Cardiff (2000)

  5. Bertsimas, D., Tsitsiklis, J.N.: Introduction to Linear Optimization. Athena Scientific, Belmont (1997)

    Google Scholar 

  6. Bianchi, G., Bruni, R., Reale, A.: Information reconstruction via discrete optimization for agricultural census data. Appl. Math. Sci. 6(125), 6241–6251 (2012)

    Google Scholar 

  7. Bomze, I.M., Locatelli, M.: Separable standard quadratic optimization problems. Optim. Lett. 6(5), 857–866 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bourbaki, N.: Topological vector spaces. Springer, Berlin (1987)

    Book  MATH  Google Scholar 

  9. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  10. Bruni, R.: Discrete models for data imputation. Discrete Appl. Math. 144(1), 59–69 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  11. Bruni, R.: Error correction for massive data sets. Optim. Methods Softw. 20(2–3), 295–314 (2005)

    MathSciNet  Google Scholar 

  12. Bruni, R., Bianchi, G.: A formal procedure for finding contradictions into a set of rules. Appl. Math. Sci. 6(126), 6253–6271 (2012)

    MATH  MathSciNet  Google Scholar 

  13. De Waal, T.: Computational Results with Various Error Localization Algorithms. UNECE Statistical Data Editing Work Session, Madrid (2003)

    Google Scholar 

  14. De Waal, T., Pannekoek, J., Scholtus, S.: Handbook of Statistical Data Editing and Imputation. Wiley Handbooks in Survey Methodology. John Wiley & Sons, Inc., New York (2011)

    Book  Google Scholar 

  15. European Council Regulation (EEC) No 357/79 of 5 February 1979 on statistical surveys, EEC Documentation (1979)

  16. Fellegi, I.P., Holt, D.: A systematic approach to automatic edit and imputation. J. Am. Stat. Assoc. 71, 17–35 (1976)

    Article  Google Scholar 

  17. Fuller, W.A.: Measurement Error Models. Wiley Series in Probability and Statistics. John Wiley & Sons, Inc., New York (2006)

    Google Scholar 

  18. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co, San Francisco (1979)

    MATH  Google Scholar 

  19. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer, New York (2001)

    Book  Google Scholar 

  20. Hochbaum, D.S., Shanthikumar, J.G.: Convex separable optimization is not much harder than linear optimization. J. ACM. 37(4), 843–862 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  21. IBM: Ilog Concert Technology 12.1 Reference Manual. International Business Machines Corporation (2009)

  22. IBM: Ilog Cplex 12.1 Reference Manual. International Business Machines Corporation (2009)

  23. Kalantari, B., Lari, I., Ricca, F., Simeone, B.: On the complexity of general matrix scaling and entropy minimization via the RAS algorithm. Math. Program. Ser. A. 112, 371–401 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  24. Klösgen, W., Żytkow, J.M. (eds.): Handbook of Data Mining and Knowledge Discovery. Oxford University Press, Oxford (2002)

    MATH  Google Scholar 

  25. Lyberg, L.E., Biemer, P., Collins, M., De Leeuw, E.D., Dippo, C., Schwarz, N., Trewin, D. (eds.): Survey Measurement and Process Quality, Section C, post survey processing and operations. John Wiley & Sons, Inc., New York (1997)

    Google Scholar 

  26. Mucherino, A., Papajorgji, P., Pardalos, P.M.: Data Mining in Agriculture. Springer, New York (2009)

    Book  MATH  Google Scholar 

  27. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. John Wiley & Sons, Inc., New York (1999)

    MATH  Google Scholar 

  28. Riera-Ledesma, J., Salazar-Gonzalez, J.J.: New Algorithms for the Editing and Imputation Problem. UNECE Statistical Data Editing Work Session, Madrid (2003)

  29. Ramakrishnan, R., Gehrke, J.: Database Management Systems (3rd edn). McGraw-Hill, New York (2003)

    Google Scholar 

  30. Schneider, M.H., Zenios, S.A.: A comparative study of algorithms for matrix balancing. Oper. Res. 38(3), 439–455 (1990)

    Article  MATH  Google Scholar 

  31. Schrijver, A.: Combinatorial Optimization. Springer, Berlin/New York (2003)

    MATH  Google Scholar 

  32. Winkler, W.E.: State of statistical data editing and current research problems. In: Proceedings of the Workshop on Data Editing. UN/ECE, Rome (1999)

Download references

Author information

Authors and Affiliations

  1. Dip. per i Censimenti e gli Archivi Amm. e Statistici (DICA), Istat, Viale Oceano Pacifico 171, 00144 , Rome, Italy

    Gianpiero Bianchi & Alessandra Reale

  2. Dip. di Ingegneria Informatica, Automatica e Gestionale (DIAG), Università di Roma “Sapienza”, Via Ariosto 25, 00185 , Rome, Italy

    Renato Bruni

Authors
  1. Gianpiero Bianchi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Renato Bruni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alessandra Reale
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Renato Bruni.

Additional information

Work developed during the biennial research collaboration between the Italian Statistic Office (Istat) and the University of Roma “Sapienza” on the data processing of the 2010 Census of Italian Agriculture.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bianchi, G., Bruni, R. & Reale, A. Balancing of agricultural census data by using discrete optimization. Optim Lett 8, 1553–1565 (2014). https://doi.org/10.1007/s11590-013-0652-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-013-0652-3

Keywords

Search

Navigation