Stochastic production planning problems were studied in several works; the
model with one production good was discussed in [3]. The extension to several
economic goods is not a trivial issue as one can see from the recent works [4],
[5] and [6]. The following qualitative aspects of the problem are analyzed in
[5]; the existence of a solution and its characterization through dynamic
programming/HJB equation, as well as the verification (i.e., the solution of
the HJB equation yields the optimal production of the goods). In this paper, we
stylize the model of [4] and [5] in order to provide some quantitative answers
to the problem. This is possible especially because we manage to solve the HJB
equation in closed form. Among other results, we find that the optimal
production rates are the same across all the goods and they also turn to be
independent of some model parameters. Moreover we show that production rates
are increasing in the aggregate number of goods produced, and they are also
uniformly bounded. Numerical experiments show some patterns of the output.