We present an analytical upper bound on the number of required vehicles for vehicle routing problems with split deliveries and any number of capacitated depots. We show that a fleet size greater than the proposed bound is not achievable based on a set of common assumptions. This property of the upper bound is proved through a dynamic programming approach. We also discuss the validity of the bound for a wide variety of routing problems with or without split deliveries.

中文翻译：

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车辆路径问题中车队规模的分析界限：一种动态规划方法

我们提出了车辆路线问题所需车辆数量的分析上限，这些车辆路线问题具有拆分交付和任意数量的有能力的仓库。我们表明，基于一组常见假设，无法实现大于提议界限的车队规模。上界的这个性质是通过动态规划方法证明的。我们还讨论了有或没有拆分交付的各种路由问题的边界的有效性。