Multiple Criteria Public Investment Decision Making by Mixed Integer Programming

  • Jeremy F. Shapiro
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 130)


Multicriterion optimization has long been an integral part of quantitative models for public planning. The models which have received the most attention consist of concave utility functions to be maximized (in a vector sense) subject to convex constraints. The convex structure of such models permits the development of complete theories characterizing efficient solutions, and well-behaved algorithms for finding these solutions.


Dual Problem Efficient Solution Duality Theory Mixed Integer Programming Model Concave Utility Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bell, D.E., (1973a), “The Resolution of Duality Gaps in Discrete Optimization”, Tech Report No. 81, Operations Research Center, Massachusetts Institute of Technology.Google Scholar
  2. 2.
    Bell, D.E., (1973b), “Improved Bounds for Integer Programs: A Supergroup Approach,” IIASA RM-73–5, International Institute for Applied Systems Analysis, Laxenburg, Austria (to appear in SIAM J. on Applied Math). Google Scholar
  3. 3.
    Bell, D.E., and J.F. Shapiro (1975), “A Finitely Convergent Duality Theory for Zero-One Integer Programming”, Operations Research Center Working Paper No. OR 043–75, Massachusetts Institute of Technology.Google Scholar
  4. 4.
    Bhatia, R., (1975), “Investment Planning for Petroleum and Fertilizer Industries; An Interregional Programming Model for India”, Center for Population Studies Report, Harvard University.Google Scholar
  5. 5.
    Dorfman, R., and H.D. Jacoby (1972), “An Illustrative Model of a Regional Water Quality Authority”, in R. Dorfman, H.D Jacoby, and H. A. Thomas, Jr. (eds.), Models for Managing Regional Water Quality Harvard University Press.Google Scholar
  6. 6.
    Evans, J.P. and R.E. Steuer (1973), “A Revised Simplex Method for Linear Multiple Objective Programs”, Mathematical Programming Vol. 5, 1, (August), 54–72.Google Scholar
  7. 7.
    Fisher, M.L., and J.F. Shapiro (1974), “Constructive Duality in Integer Programming”, SIAM Journal on Applied Mathematics 27, 31–52.Google Scholar
  8. 8.
    Fisher, M.L.,W.D. Northup and J.F. Shapiro (1974), “Using Duality to Solve Discrete Optimization Problems: Theory and Computational Experience”, Operations Research Center Working Paper No. OR 030–74, Massachusetts Institute of Technology (to appear in Mathematical Programming).Google Scholar
  9. 9.
    Geoffrion, A.M., J.S. Dyer and A.Feinberg, (1972), “An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department”, Management Science Vol. 19, pp. 357–368.Google Scholar
  10. 10.
    Glover, F., (1969), “Integer Programming over a Finite Additive Group”, SIAM Journal on Control 7, 213–231.Google Scholar
  11. 11.
    Goreux, L.M., and A. S. Manne (1973), Multi-level Planning; Case Studies in Mexico, North-Holland.Google Scholar
  12. 12.
    Garry G.A., W.D. Northup, and J.F. Shapiro (1973), “Computational Experience with a Group Theoretic Integer Programming Algorithm”, Mathematical Programming 4, 171–192.Google Scholar
  13. 13.
    Karlin, S. (1959), Mathematical Methods and Theor in Games, Programming and Economics Volume 1, Addison-WesleyGoogle Scholar
  14. 14.
    Kendrick, D., and A. Stoutjesdijk (1975), The Planning of industrial Investment Programs; A Methodology (Manuscript in progress).Google Scholar
  15. 15.
    Kuhn, H.W., and A. W. Tucker (1950), “Nonlinear Programming”, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, California, pp. 481–492.Google Scholar
  16. 16.
    Kuhner, J., and J.J. Harrington (1974), “Large-Scale Mixed Integer Programming for Investigating Multi-Parity Public Investment Decisions: Application to a Regional Solid Waste Management Problem”, (presented at 45th National ORSA/TIMS Meeting, Boston).Google Scholar
  17. 17.
    Magnanti, T.L., J.F. Shapiro and M.H. Wagner (1973), “Generalized Linear Programming Solves the Dual”, Operations Research Center Working Paper, No. 019–73, Massachusetts Institute of Technology, (to appear in Management Science.Google Scholar
  18. 18.
    Lasdon, L.S., (1970), Optimization Theory for Large Systems Macmillan.Google Scholar
  19. 19.
    Marks, D.H. (1974), “Modelling for Policy Analysis in a Large Scale Underdeveloped River Basin”, (presented at ORSA/TB4S Meeting, April, 1974, Boston).Google Scholar
  20. 20.
    Shapiro, J.F. (1968), “Dynamic Programming Algorithms for the Integer Programming Problem - I: The Integer Programming Problem Viewed as a Knapsack Type Problem”, Operations Research 16, 103–121.Google Scholar
  21. 21.
    )Shapiro, J.F., “Generalized Lagrange Multipliers in Integer Programming”, Operations Research 19, 68–76.Google Scholar
  22. 22.
    )Shapiro, J.F., “A New Duality Theory for Mixed Integer Programming”, Operations Research Center Working Paper No. OR 033–74, Massachusetts Institute of Technology (to appear in the Proceedings of the Congress on Mathematical Programming and Its Applications, Rome, April, 1974.Google Scholar
  23. 23.
    Westphal, L.E. (1971), Planning Investments with Economies of Scale North-HollandGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • Jeremy F. Shapiro

There are no affiliations available

Personalised recommendations