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.

翻译：本文的主要贡献在于提出了一种解决连续时间联合补货问题的新算法方法，称为Ψ-成对对齐。该机制通过同步多个经济订货量模型，使我们能够设计一种纯组合算法，以任意精度有效逼近最优策略。因此，我们的工作构成了自20世纪80年代中期以来在该领域处于领先地位的2的幂次策略的首次定量改进。此外，鉴于近期出现的难解性结果，通过提出一种针对联合补货问题的高效多项式时间近似方案（EPTAS），我们解决了这一经典设置中长期存在的计算复杂性公开问题。