A note on the multidimensional dual

• Published in: European journal of operational research Vol. 17; no. 1; pp. 116 - 122
• Main Author: Ignizio, James P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.01.1984; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: Algorithms; Dual; Goal programming; Linear programming
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/0377-2217(84)90014-6

Lexicographic linear goal programming (i.e., the specific form of goal programming wherein one seeks the lexicographic minimum of an ordered set of goal deviations) represents one of the most common and, evidently, widely used forms of goal programming. This form, also described as linear goal programming with a ‘preemptive priority’ structure, has also engendered considerable interest in the literature. However, the dual of the lexicographic linear goal programming model has, thus far, received only minimal exposure. This despite the fact that this dual was developed more than ten years ago. The purpose of this note is to provide a single, unified presentation of the fundamental notion of duality in lexicographic linear goal programming and to indicate existing as well as potential exploitations of this concept.