Continuous-time production control under periodic inventory review

In this paper, we consider a single-machine production system, operating under a stochastic demand. Over each production cycle, it is assumed that there is a single realization of the demand random variable. Furthermore, it is assumed that the system is operated under a periodic-review policy. Thus, the particular realization of the demand cannot be determined prior to the end of the corresponding period. The continuous-time optimal production control, that minimizes a linear combination of expected surplus and shortage costs over the planning horizon is shown to be piecewise constant, and the appropriate production levels and control breakpoints are determined as functions of the demand distribution.