Summary
The class of programming problems with maximin objective function may be expressed as: maximizeZ=min (C 1 X, C 2 X,...,C n X) subject toAX=b, X⩾0.
This class is wider than the class of problems studied recently byKaplan [1974] who has also justified their consideration on the ground that some practical problems of interest have this structure. The purpose of this note is to show that with the help of a suitable transformation, the above class of problems can be transformed to the type of problems studied byKaplan.
Zusammenfassung
Wir betrachten folgende Klasse von Problemen: MaximiereZ:= min (C 1 X, C 2 X,..., C n X) unter den NebenbedingungenAX=b, X⩾0. Diese Klasse ist weiter als die vonKaplan [1974] betrachtete und motivierte Problemklasse. Der Zweck dieser Note ist, zu zeigen, daß mit einer geeigneten Transformation die hier betrachtete Problemklasse auf die vonKaplan untersuchte Klasse zurückgeführt werden kann.
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References
Kaplan, S.: Applications of Programs with maximin objective function to problems of optimal resource allocation. Operations Research22 (4), 1974.
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Gupta, R., Arora, S.R. Programming problems with maximin objective function. Zeitschrift für Operations Research 22, 69–72 (1978). https://doi.org/10.1007/BF01917645
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DOI: https://doi.org/10.1007/BF01917645