The Continuous-Time Joint Replenishment Problem: ε-Optimal Policies via Pairwise Alignment

The main contribution of this paper resides in developing a new algorithmic approach for addressing the continuous-time joint replenishment problem, termed Ψ-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-1980s. Moreover, in light of recent intractability results, by proposing an efficient polynomial-time approximation scheme for the joint replenishment problem, we resolve the long-standing open question regarding the computational complexity of this classical setting.