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Surrogate constraints. (English) Zbl 0165.22602

Summary: A surrogate constraint is an inequality implied by the constraints of an integer program, and designed to capture useful information that cannot be extracted from the parent constraints individually but is nevertheless a consequence of their conjunction. The use of such constraints as originally proposed by the author has recently been extended in an important way by Egon Balas [Oper. Res. 13, 517–546 (1965; Zbl 0194.19903)] and Arthur M. Geoffrion [SIAM Rev. 9, 178–190 (1967; Zbl 0213.44702)]. Motivated to take advantage of information disregarded in previous definitions of surrogate constraint strength, we build upon the results of Balas and Geoffrion to show how to obtain surrogate constraints that are strongest according to more general criteria. We also propose definitions of surrogate constraint strength that further extend the ideas of the author [Oper. Res. 13, 879–919 (1965; Zbl 0163.41301)] by means of “normalizations”, and show how to obtain strongest surrogate constraints by reference to these definitions also.

MSC:

90C10 Integer programming
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