Multiple Objective Linear Programming: An Economist’s Perspective
Conference paper
Abstract
This paper discusses the MOLP problem as a generalization of the linear activity analysis model of Koopmans. In this model each objective function measures the quantity of some good or service which is traded in a market; the constraints in the problem arise from non-traded goods and services. The economic concepts of feasible, technically efficient and economically efficient transformations are introduced. The relationships between market prices for traded goods and services and the shadow prices of non-traded goods is described. The economic content of the MOLP model of production is summarized by four mappings.
Keywords
Linear Programming Problem Shadow Price Price Vector Relative Interior Revenue Function
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References
- 1.Bitran, Gabriel R., “Duality for Nonlinear Multiple Criteria Optimization Problems”, Technical Report No. 155, Operations Research Center, Massachusetts Institute of Technology, September 1978.Google Scholar
- 2.Duesing, Erick C., “An Open Dynamic Linear Activity Analysis Model of Production” in I. Kavrakoglu, ed., Mathematical Modelling of Energy Systems, No. 37, NATO Advanced Study Institute Series: Applied Science, Sijthoff & Noordhoff, 1980.Google Scholar
- 3.Duesing, Erick C., “A Two Level Algorithm for Multiple Objective Linear Programming”, Paper presented at the Tenth International Symposium on Mathematical Programming, Montreal, August 27–31, 1979.Google Scholar
- 4.Duesing, Erick C., Polyhedral Convex Sets and the Economic Analysis of Production, Unpublished Ph.D. Dissertation, Department of Economics, University of North Carolina, Chapel Hill, 1978. Abstract in Dissertation Abstracts International, Volume 39A (May, 1979), p. 6891-A.Google Scholar
- 5.Griffin, Victor, Polyhedral Polarity, Unpublished Ph.D. Dissertation, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, 1977.Google Scholar
- 6.Isermann, Heinz, “The Relevance of Duality in Multiple Objective Linear Programming”, Tims Studies in the Management Sciences, 6 (1979), pp. 241–262.Google Scholar
- 7.Koopmans, Tjalling C., “Analysis of Production as an Efficient Combination of Activities”, in T. C. Koopmans, ed., Activity Analysis of Production and Allocation, Wiley, 1951, pp. 33-97.Google Scholar
- 8.Kornbluth, J. S. H., “Accounting in Multiple Objective Linear Programming”, The Accounting Review, (April, 1974), pp. 284-295.Google Scholar
- 9.Kornbluth, J. S. H., “Duality, Indifference and Sensitivity Analysis in Multiple Objective Linear Programming”, Operational Research Quarterly, 25 (1974), pp. 599–614.CrossRefGoogle Scholar
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© Springer-Verlag Berlin Heidelberg 1981