Bounding Multiple Objective Linear Programming objective functions: effect on efficient set size

In multiple objective linear programming problems the extraction of all the efficient extreme points becomes problematic as the size of the problem increases. One of the suggested actions, in order to keep the size of the efficient set to manageable limits, is the use of bounds on the values of the objective functions by the decision maker. The unacceptable efficient solutions are screened out from further investigation and the size of the efficient set is reduced. Although the bounding of the objective functions is widely used in practice, the effect of this action on the size of the efficient set has not been investigated. In this paper, we study the effect of individual and simultaneous bounding of the objective functions on the number of the generated efficient points. In order to estimate the underlying relationships, a computational experiment is designed, in which randomly generated multiple objective linear programming problems of various sizes are systematically examined.