Simple Models in Stochastic Production Planning.

Abstract : A simple stochastic production-inventory model with quadratic cost functions is analyzed in detail. The inventory process is assumed to be driven by a white noise process resulting into an Ito stochastic differential equation. Both finite and infinite horizon versions of the problem are treated by a methodology based on the theory of stochastic integrals and differentials. Particular attention is given to illustrate the methodology, which is quite general and capable of dealing with more complicated problems. The paper concludes with some remarks in connection with the relationship of the results of this paper to the results in the deterministic case. (Author)