The Continuous Periodic Joint Replenishment Problem (CPJRP) has been one of the core and most studied problems in supply chain management for the last half a century. Nonetheless, despite the vast effort put into studying the problem, its complexity has eluded researchers for years. Although the CPJRP has one of the tighter constant approximation ratio of 1.02, a polynomial optimal solution to it was never found. Recently, the discrete version of this problem was finally proved to be NP-hard. In this paper, we extend this result and finaly prove that the CPJRP problem is also strongly NP-hard.

中文翻译：

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连续联合补货问题是强 NP-Hard

连续周期性联合补货问题（CPJRP）是近半个世纪以来供应链管理中研究最多的核心问题之一。尽管如此，尽管为研究这个问题付出了巨大的努力，但其复杂性多年来一直困扰着研究人员。尽管 CPJRP 具有更严格的常数近似比 1.02 之一，但从未找到它的多项式最优解。最近，这个问题的离散版本终于被证明是 NP-hard。在本文中，我们扩展了这个结果并最终证明了 CPJRP 问题也是强 NP-hard 问题。