The optimal frozen period in a dynamic production model

We consider a periodic auditing model for manufacturers in a supply chain, who observe stochastic demand, proportional holding/expedited ordering costs, and setup cost. Customer demand for a component can arrive in any period, but the procurement quantities are determined every T periods, which is defined as a frozen period. The demand forecasts are updated every period as more information becomes available from the marketplace. This paper studies a forecast order policy and compares it with the optimal order policy. Our objective is to determine the optimal length of a frozen period and the safety stock in a frozen period such that the expected total cost per unit of time is minimized.