The proposed model can be extended to some more
general settings. For example, some other parameters of
the model, like the unit holding cost per period, might
also evolve according to continuous-time Markov processes.
In this case, ht would be equal to ict+wt, where i is
the inventory carrying cost rate and wt is the unit storage
cost at the beginning of period t. It can be assumed that
the unit storage cost evolves according to another
continuous-time Markov process, which is independent
of the continuous-time Markov process corresponding to
the evolution of the unit production cost. There are two
state variables in this new problem. The first is the unit
production cost, the same as that of the original problem,
and the second is the unit storage cost. Finally, the DP
functional equation (8) can be extended to obtain the optimal production scheduled for each period, in this new
problem.