Surrogate Constraints

A surrogate constraint is an inequality implied by the constraints of an integ~r program, and designed to capture useful information that cannot be extra~ted from the parent constraints individually but is nevertheless a consequepce of their conjunction. The use of such constraints as originally propo~ed by the author has recently been extended in an important way by EGON! BALAS and ARTHUR GEOFFRION. Motivated to take advantage of info~ation 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 in 1965 by means of 'normalizations,' and show how to obtain strongest surrogate constraints by reference to these defini~ions also.