Mathematical Methods for Multilevel Planning

Technical Report No. 79-2
February 1979

Wayne F. Bialas
and
Mark H. Karwan

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Abstract

The general multilevel programming problem is a set of nested optimization problems over a single feasible region. Control over the decision variables is partitioned among the levels, but a decision variable may impact the objective function of several, if not all, levels. This approach is applicable to a variety of water resource planning problems, and will be compared to previous methods of multilevel planning.

Key words: bilevel programming, Pareto inefficiency, multilevel linear programming, multilevel optimization

Notes

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Bibliography for this paper

Abernathy, W.J., B. Nicholas, J.C. Hershey and S. Wandel, A Three-Stage Manpower Planning and Scheduling Model - A Service-Sector Example,  Operations Research, Vol.21, No.3, 1973, pp.693-711

Balas, E., An Infeasibility Pricing Decomposition Methods for Linear Programs, Operations Research, Vol.14, No.5, September-October 1966, pp.847-873

Baker, N.R., W.E. Sanders, C.R. Shumway, P.M. Maher, and A.H. Rubenstein, A Budget Allocation Model for Large Hierarchical R&D Organizations,  Management Science, Vol.23, No.1, September 1976, pp.59-70.

Basar, T., On the Relative Leadership Property of Stackelberg Strategies, Journal of Optimization Theory and Applications, Vol.11, No.6, 1973, pp.655-661.

Baumol, W.J. and T. Fabian, Decomposition, Pricing for Decentralization and External Economies, Management Science, Vol.11,September 1964, pp.1-32.

Benayoum, R., J. Montgolfier, J. Tergny and O. Laritchev, Linear Programming with Multiple Objectives: STEP Methods (STEM),  Mathematical Programming, Vol.1, 1971.

Bracken, J. and J.T. McGill, Mathematical Programs with Optimization Problems in the Constraints,  Operations Research, Vol.21, 1973, pp.37-44.

Candler, W. and R. Norton, Multilevel Programming, unpublished research memorandum, DRC, World Bank, Washington, D.C., August 1976.

Cassidy, R., M.J. Kirby and W.M. Raike, Efficient Distribution of Resources Through Three Levels of Government,  Management Science, Vol.17, No.8, April, 1972, pp.462-473.

Charnes, A., R.W. Clower and K.O. Kortanek, Effective Control Through Coherent Decentralization with Preemptive Goals,  Econometrica, Vol.35, No.2, April 1967, pp.294-319. 

Charnes, A. and W. Cooper, Management Models and Industrial Applications of Linear Programming, John Wiley & Sons, 1961.

Cooper W.W., H.J. Leavitt and M.W. Shelly II, New Perspectives in Organization Research, John Wiley & Sons, 1964.

Cruz, J.B., Stackelberg Strategies for Multilevel Systems, in Directions in Decentralized Control, Many Person Optimization and Large-Scale Systems, Y.C. Ho and S.K. Mitter, Eds., new York, Plenum Press, 1976, pp.139-147.

Cruz, J.B., Leader-Follower Strategies for Multilevel Systems, IEEE Transactions on Automatic Control, Vol.AC-23, April, 1978, pp.244-255.

Davis, W. and J. Talavage, Three-Level Models for Hierarchical Coordination,  OMEGA, The International Journal of Management Science, Vol.5, No.6, pp.709-720.

Dantzig, G.B. and P. Wolfe, Decomposition Principle for Linear Programs," Operations Research, Vol.8, No.1, 1960, pp.101-111.

Freeland, J. and N. Baker, Goal Partitioning in a Hierarchical Organization,   The International Journal of Management Science, Vol.3, No.6, 1975, pp.673-678.

Freeland, J. and J. Moore, Some Organizational Properties of Resource Directive Allocation Mechanisms,  Research Paper No.389, Stanford University, October 1975.

Geoffrion, A., Primal Resource-Directive Approaches for Optimizing Non-Linear Decomposable Systems,  Operations Research, Vol.18, No.3, May-June, 1970.

Geoffrion, A., Elements of Large Scale Mathematical Programming,  Management Science, Vol.16, No.11, July, 1970, pp.652-691.

Geoffrion, A., Large Scale Linear and Nonlinear Programming,  in Optimization Methods for Large Scale Systems, David A, Wismes, Ed., McGraw-Hill Book Company, 1971, pp.75-120.

Geoffrion, A., J. Dyer and A. Feinberg, An Interactive Approach for Multi-Criterion Optimization of an Academic Department,  Management Science, Vol.19, No.4, December, 1972, Part 1, pp.357-368.

Geoffrion, A. and W. Hogan, Coordination of Two Level Organization with Multiple Objectives,  in Balakrishnan, A.V., Ed., Techniques of Optimization, Academic Press, 1972.

Goreaux, L. M. and A.S. Manne, Multi-Level Planning: Case Studies in Mexico, North-Holland, Amsterdam, 1973.

Haimes Y.Y., J. Foley and W. Yu, Computational Results for Water Pollution Taxation Using Multilevel Approach,  Water Resources Bulletin, Vol.8, No.4, August, 1972, pp.761-771.

Haimes Y.Y, W.A. Hall and H.T. Freedman, Multiobjective Optimization in Water Resources Systems, Elsevier, Amsterdam, 1975.

Keeney, R.L. and H. Raiffa, Decision with Multiple Objectives: Preferences and Value Trade-offs, John Wiley, New York, 1976.

Koopmans, T., Analysis of Production as an Efficient Combination of Activities,  in Koopmans, T.C., Ed. Activity Analysis of Production and Allocation, John Wiley, New York, 1965, pp.33-94.

Lasdon, L., Optimization Theory for Large Systems, The MacMillan Company, New York, 1970.

Maier, S.F. and J.H. VanderWeide, Capital-Budgeting in the Decentralized Firm,  Management Science, Vol.23, No.4, December, 1976, pp.433-443.

Mathews, J.A., Primal and Dual Game Theoretic Solution with Application to Decentralized Control, Working Paper, University of Rhode Island, June 1978.

Mesarovic, M., D. Macko, and Y. Takahara, Theory of Hierarchical Multi-Level Systems, Academic Press, New York, 1970.

Osteryoung, J.S., Multiple Goals in the Capital Budgeting Decision,' in Cochrane, J.L. and Zeleny, M., Eds., Multiple Criteria Decision Making, University of South Carolina Press, Columbia, S.C., 1972.

Ruefli, T., A Generalized Goal Decomposition Model,  Management Science, Vol.17, No.9, 1971.

Ruefli, T., Behavioral Externalities in Decentralized Organizations,  Management Science, Vol.17, No.5, 1971.

Ruefli, T., Linked Multicriteria Decision Models,' in Cochrane, J.L. and Zeleny, M., Eds., Multiple Criteria Decision Making, University of South Carolina Press, Columbia, S.C., 1972.

Simaan, M. and J.B. Cruz, On the Stackelberg Strategy in Nonzero-Sum Games, Journal of Optimization Theory and Applications, Vol.11, No.5, 1973, pp.533-555.

Steuer, R.E., Multiple Objective Linear Programming with Interval Criteria Weights, Management Science, Vol.23, 1976.

Whinston, A., Pricing Guides in Decentralized Organization, in W. Cooper, et al., Eds., New Perspectives in Organization Research, John Wiley & Sons, New York, 1964.

Yu, P.L. and M. Zeleny, The Set of all Nondominated Solutions in Linear Cases and a Multicriteria Simplex Method,  Journal of Mathematical Analysis and Applications, Vol. 49, 1975.

Zionts, S. and J. Wallenius, In Interactive Programming Method for Solving the Multiple Criteria Problem, Management Science, Vol.22, 1976.

Zionts, S., A Survey of Multiple Criteria Integer Programming Methods, paper presented at the DO77 conference, University of British Columbia, 1977. 

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