On the equivalence of control theoretic, differential, and difference equation approaches to modeling supply chains

We conduct an analysis of an ordering and inventory control algorithm in both continuous and discrete time for a production and inventory control system employing a generalized order-up-to policy. We demonstrate that the management insights gained from both the continuous and discrete time approaches are very similar, and conclude that for practical purposes we may use either time domain in an analysis. This is particularly useful as questions that are difficult to analyze in one time domain may be easier in the other. Although the exact results may differ, their qualitative nature is essentially equivalent.