While most supply chain models assume linearity, real production and distribution systems often operate in constrained contexts. This article aims to analyse the consequences of capacity limits in the order-up-to replenishment policy with minimum mean squared error forecasting under independently and identically distributed random demand. Our study shows that the impact of this nonlinearity is often significant and should not be ignored. In this regard, we introduce the concept of a settling capacity, which informs when our knowledge from a linear analysis is a reasonable approximation in a nonlinear context. If the available capacity is less than the settling capacity, the nonlinear effects can have a significant impact. We compare the Bullwhip Effect and Fill Rate in constrained contexts to well-established results for linear supply chains. We reveal the capacity limit acts as a production smoothing mechanism, at the expense of increasing inventory variability. We proceed to analyse the economic consequences of the capacity constraint and show that it can actually reduce costs. We provide an approximate solution for determining the optimal capacity depending on the demand, the unit costs and the lead time.
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