Minimization of a Piecewise Quadratic Function Arising in Production Scheduling

In the study of production scheduling to meet random fluctuations in supply and demand, a probabilistic measure of effectiveness can be used. This measure is a piecewise quadratic positive definite function having discontinuous derivatives at a finite number of points. The unique minimum of this function, which always exists, can be found by applying an algorithm resembling the simplex algorithm. The computations per iteration are longer and the logic more complicated than for the simplex algorithm. The method can be applied to any overdetermined system in which all of the critical variables are functions of a single adjustable variable. The system is assumed to be linear and the input disturbances are presumed Gaussian.