Abstract
A wide variety of applied problems involve programs trading off one objective against another, such as time versus cost. The present article does this by interchanging the objective function and one constraint. The approach is a practical formulation of the bi-objective program. We state the correspondences between the primal and dual solution sets: under certain conditions the primal solution sets correspond and dual solution sets coincide or are equivalent. The article concludes with numerical illustrations and a large-scale application to portfolio analysis.
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Research initiated at the Australian National University during my tenure of the Professorial Fellowship in Economic Policy of the Reserve Bank of Australia. I am greatly indebted to Mr. M. Young of Young & Co., Sharebrokers, New Zealand Stock Exchange, for access to the data base of Section 5 and to Mrs. J. Goldsmith (Massey University) for organizing the entire computer exercise. Helpful comments by Professor K. A. Fox (Iowa State University) and Dr. F. vande Ginste (Science Foundations, Brussels), and numerical assistance by Miss S. Guthrie (Massey University) are gratefully acknowledged.
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van Moeseke, P. Applied Bi-objective programs. Zeitschrift für Operations Research 31, B31–B54 (1987). https://doi.org/10.1007/BF01272655
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DOI: https://doi.org/10.1007/BF01272655