ABSTRACT
In this chapter, we shall discuss applications of pseudolinear functions and their properties, especially in hospital management, economics, and in developing simplex-type algorithms for quadratic fractional programming problems. In the first section, we present the studies of Kruk and Wolkowicz [150]. Kruk and Wolkowicz [150] have revisited and reformulated the hospital management problem studied by Mathis and Mathis [180] to provide the mathematical background and convergence proof for the algorithm. Kruk and Wolkowicz have slightly modified the algorithm of Mathis and Mathis [180] and explained that the cause of simplicity of the algorithm is that its objective function is a pseudolinear function. They have shown that the hospital management problem described by Mathis and Mathis [180] falls into the class of linear constrained pseudolinear optimization problems. The study of Kruk and Wolkowicz justifies the significance of the class of pseudolinear functions and related programming problems. Kruk and Wolkowicz have remarked that this could only be possible by using the properties of pseudolinear functions. Moreover, in the case of a stationary point, the behavior of a pseudolinear function is as good as a linear function. The properties of this class of functions have helped to conclude that: The simplex method is much more than its tableau representation, and the class of problems to which it applies is much larger than that of linear programs.
