Mathematical Programming

  • Richard Valliant
  • Jill A. Dever
  • Frauke Kreuter
Part of the Statistics for Social and Behavioral Sciences book series (SSBS)


Most surveys of any size are multipurpose—many important variables, different estimation needs (means, totals, model parameters, etc.) and various domains or subpopulations. Minimum sample sizes may be set for the domains, along with precision constraints for the estimates. Above all, there is usually a limited amount of money available. Multiple goals and constraints mean that the allocation problem is considerably more complicated than was presented in earlier chapters. These goals and constraints can be accommodated using the techniques of mathematical programming that are illustrated using the Solver tool in Excel, the nloptr and alabama packages in R, and the optmodel and nlp procedures in SAS.


  1. Dantzig G. B. (1963). Linear Programming and Extensions. Princeton University Press, Princeton, NJ.zbMATHGoogle Scholar
  2. Freund R. (1994). Professor George Dantzig: Linear programming founder turns 80. SIAM News.Google Scholar
  3. Gomes H., Johnson W. (2016). Sample size optimization of the consumer price index: An implementation using R. In: Proceedings of the Business and Economic Statistics Section, American Statistical Association, pp 2137–2151.Google Scholar
  4. Johnson S. (2014). The NLopt nonlinear-optimization package. URL
  5. Lange K. (2004). Optimization. Springer, New York.CrossRefGoogle Scholar
  6. Leaver S., Solk D. (2005). Handling Program Constraints in the Sample Design for the Commodities and Services Component of the U.S. Consumer Price Index. In: Proceedings of the Survey Research Methods Section, American Statistical Association, pp 2024–2028, URL
  7. Madsen K., Nielsen H. B., Tingleff O. (2004). Optimization with constraints, 2nd edn. Tech. rep., Technical University of Denmark, URL Google Scholar
  8. Powell S. G., Baker K. R. (2003). The Art of Modeling with Spreadsheets: Management Science, Spreadsheet Engineering, and Modeling Craft. John Wiley & Sons, Inc., New York.Google Scholar
  9. Svanberg K. (2002). A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM Journal of Optimization 12(2):555–573.MathSciNetCrossRefGoogle Scholar
  10. Varadhan R. (2015). alabama: Constrained nonlinear optimization. URL, note = R package version 2015.3-1.
  11. Winston W., Venkataramanan M. (2003). Introduction to Mathematical Programming, 4th edn. Duxbury Press, Pacific Grove, CA.Google Scholar
  12. Ypma J. (2014). nloptr: R interface to NLopt. URL

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Richard Valliant
    • 1
    • 2
  • Jill A. Dever
    • 3
  • Frauke Kreuter
    • 2
    • 4
  1. 1.University of MichiganAnn ArborUSA
  2. 2.University of MarylandCollege ParkUSA
  3. 3.RTI InternationalWashington, DCUSA
  4. 4.University of MannheimMannheimGermany

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