Numerical approximation to solve QVI systems related to some production optimization problems

ARAGONE, L.; MANCINELLI, E.

Handbook of Optimization Theory: Desition Analysis and Applications

Nova Science Publishers, Inc.

Año: 2010; p. 329 - 376

In this paper we develop numerical procedures to solve Quasi Variational Inequalities(QVI) Systems which appear in the optimization of some problems related to amulti-item single machine, which at any time the machine is either idle or producingany of m different items. Our aim is to obtain an optimum production schedule foreach of the cases we propose.We focus our attention on three cases: the discount case, where the cost to be optimizedtakes into account a running cost and the production switching costs, as theintegral cost functional has an infinite horizon a discount factor is used to guaranteethat the integral converges; the ergodic case, where the objective is to find an optimalproduction schedule that minimizes the average cost for an infinite horizon; and thepiecewise deterministic case where the demand varies randomly according to a piecewisedeterministic process, the demand changes are described by a Poisson processesand the demand value may take a finite number of values.