  This paper considers the periodic-review stochastic joint replenishment
problem (JRP) under Bookbinder and Tan's static-dynamic uncertainty control
policy. According to a static-dynamic uncertainty control rule, the decision
maker fixes timing of replenishments once and for all at the beginning of the
planning horizon, the inventory position is then raised to a predefined
order-up-to-position at the beginning of each replenishment period. In this
policy, freezing the replenishment times ameliorates the inherent difficulties
pertinent to replenishment coordination of multiple products, whereas dynamic
order quantities facilitate dealing with uncertain demands. We adapt and extend
an earlier mixed integer linear programming (MILP) model for computing
static-dynamic uncertainty policy parameters, and demonstrate that the same can
be used to approximate the optimal control rule for the JRP, also known as
$(\sigma, \vec{S})$ policy. An extensive computational study illustrates the
effectiveness of our approach when compared to alternative approaches in the
literature.
