Optimal feeding buffers for projects or batch supply chains by an exact generalization of the newsvendor result

In project scheduling or batch supply chain operations, a positive (negative) feeding buffer is created by starting an activity before (after) its expected latest start time. Positive feeding buffers provide protection against project tardiness. Assuming linear costs for starting activities earlier and a linear project tardiness penalty, early optimization models for project buffers addressed particular project network structures. By these models it can be shown that when the gating activities precede the only stochastic elements in a project, then there exists an exact generalization of the newsvendor optimal result that characterizes the optimal feeding buffers: the marginal cost of a buffer should match its criticality. This insight is associated with an effective and efficient solution approach by simulation. We show that this result also holds when stochastic elements exist anywhere else within the project and when activities are statistically correlated. Furthermore, the same simulation approach applies. This yields practically optimal feeding buffers even when it is impossible to compute the completion time distribution.