  The main contribution of this paper resides in developing a new algorithmic
approach for addressing the continuous-time joint replenishment problem, termed
$\Psi$-pairwise alignment. The latter mechanism, through which we synchronize
multiple Economic Order Quantity models, allows us to devise a
purely-combinatorial algorithm for efficiently approximating optimal policies
within any degree of accuracy. As a result, our work constitutes the first
quantitative improvement over power-of-$2$ policies, which have been
state-of-the-art in this context since the mid-80's. Moreover, in light of
recent intractability results, by proposing an efficient polynomial-time
approximation scheme (EPTAS) for the joint replenishment problem, we resolve
the long-standing open question regarding the computational complexity of this
classical setting.
