Abstract
The multiple objective linear programming problem is interpreted here as a model of production for a multiproduct firm operating in competitive markets. Feasible and nondominated values of the objective functions in the problem are characterized by means of a polyhedral cone which is dual to the cone generated by the problem data. The generators of extreme rays of the dual cone give rise to a collection of hyperplanes and their associated halfspaces whose intersection is the set of feasible objective function values. Nondominated faces of this set are characterized in terms of the coefficients of equated constraints. Tradeoffs between permissible objective function values are described, and perturbation of right hand side coefficients of the problem constraints and marginal analysis of changes in objective function values are also derived within a uniform analytical framework.
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© 1983 Springer-Verlag Berlin Heidelberg
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Duesing, E.C. (1983). Multiple Objective Linear Programming and the Theory of the Firm: I. Substitution and Sensitivity Analysis. In: Hansen, P. (eds) Essays and Surveys on Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46473-7_5
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DOI: https://doi.org/10.1007/978-3-642-46473-7_5
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