Abstract
This paper concerns a methodological reflection on the multiobjective approach to public systems which involve group decision processes. Particular attention is given to an integrated program of regional systems which include value trade-offs between multiple objectives. Our intention is to combine the judgmental processes with the optimization processes in the “soft” public systems. A two-layer approach is applied. At the first layer, each regional program is formulated in mathematical programming based on a utility assessment with different regional characteristics. Each subsystem independently reflects its particular concern as a single agent. The dual optimal solutions obtained for each subsystem are treated as an index, or the theoretical prices, representing the value trade-offs among the multiple objectives. At the second layer, an effective formation of interregional cooperation for compromising the conflicting regional interests is examined. Ann-person cooperative game in the characteristic function form is used to evaluate the effectiveness of the cooperation. The characteristic function for the game is derived on the incremental value of the regional benefit after the formation of a cooperation. The nucleolus and the augmented nucleolus as the solution concepts of the cooperative game are used for indicating the effectiveness of the cooperation. Finally using alternative criteria, the results in assessing the best decisions are examined comparatively.
Similar content being viewed by others
References
A.V. Fiacco,Introduction to Sensitivity and Stability Analysis in Nonlinear Programming (Academic Press, New York, 1983).
A. Kopelowitz, “Computation of the kernels of simple games and the nucleolus ofn-person games,” R.M. 31, Department of Mathematics, Hebrew University (1967).
L.S. Lasdon and A.D. Warren, “Generalized reduced gradient software for linearly and nonlinearly constrained problems,” in: H.J. Greenberg, ed.,Design and Implementation of Optimization Software (Sijthoff & Noordhoff, Alphen aan den Rijn, 1978).
S.C. Littlechild, “A simple expression for the nucleolus in a special case,”International Journal of Game Theory 3 (1) (1974) 21–29.
D.G. Luenberger,Introduction to Linear and Nonlinear Programming (Addison—Wesley, Reading, MA, 1973).
B.A. Murtagh and M.A. Saunders, “A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints,”Mathematical Programming Study 16 (1982) 84–117.
B.A. Murtagh and M.A. Saunders, MINOS 5.0 User's Guide, Technical Report SOL 83-20, Stanford University (Stanford, CA, 1983).
G. Owen, “A note on the nucleolus,”International Journal of Game Theory 3 (2) (1974) 101–103.
H. Raiffa,Decision Analysis (Addison-Wesley, Reading, MA, 1968).
M. Sakawa, K. Tada, and I. Nishizaki, “A new solution concept in a cooperativen-person game and its application,”Journal of Electronics and Communication Society J.66-A(12) (1983). [In Japanese.]
R. Schlaifer,Analysis of Decisions Under Uncertainty (McGraw-Hill, New York, 1969).
F. Seo, “Evaluation and control of regional environmental systems in the Yodo river basin: socio-economic aspects,”Proceedings of IFAC Symposium on Environmental Systems Planning, Design and Control (Pergamon, Oxford, 1978).
F. Seo, “An integrated approach for improving decision making processes,”Behavioral Science 25 (1980) 387–396.
F. Seo and M. Sakawa, “Fuzzy multiattribute utility analysis for collective choice,”IEEE Transactions on Systems, Man, and Cybernetics SMC-15 (1) (1985) 45–53.
F. Seo and M. Sakawa,Multiple Criteria Decision Analysis in Regional Planning (Reidel, Dordrecht, 1988).
L.S. Shapley and M. Shubik, “Quasi-cores in a monetary economy with nonconvex preferences,”Econometrica 34 (4) (1966) 805–827.
P. Wolfe, “Methods of nonlinear programming,” in: R.L. Graves and P. Wolfe, eds.,Recent Advances in Mathematical Programming (McGraw-Hill, New York, 1963).
P. Wolfe, “Methods of nonlinear programming,” in: J. Abadie, ed.,Nonlinear Programming (North-Holland, Amsterdam, 1967).
H.P. Young, N. Okada and T. Hashimoto, “Cost allocation in water resources development,”Water Resources Research 18 (3) (1982) 463–475.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Seo, F. Utilization of mathematical programming for public systems: An application to effective formation of integrated regional information networks. Mathematical Programming 52, 71–98 (1991). https://doi.org/10.1007/BF01582881
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01582881