In this paper, we consider a variant of the Inventory Routing Problem (IRP), the Time-Dependent IRP (TD-IRP). The TD-IRP extends the routing component of the IRP by making the travelling time between two locations no longer constant but depending on the departure time. In order to investigate the relevance of considering time-dependent travelling time functions, a set of new benchmark instances based on real-data is assumed. Numerical experiments show that optimising with time-dependent travelling times is cost-efficient, but computationally challenging. Thus, we propose a matheuristic that decomposes the problem, based on the observation of the structure of optimal TD-IRP solutions. The proposed matheuristic defines the set of clients to visit and the quantity to deliver for each period first and solves the routing problem second. Numerical experiments prove it to be very efficient and yield solutions with small gaps to the best lower bounds found. Because it separates the routing problem, the proposed matheuristic opens the possibility to solve the TD-IRP very efficiently by taking advantage of the rich literature on time-dependent routing problems.

在本文中，我们考虑库存路由问题 (IRP) 的一个变体，即时间相关 IRP (TD-IRP)。TD-IRP 扩展了 IRP 的路由组件，使两个位置之间的旅行时间不再恒定，而是取决于出发时间。为了研究考虑与时间相关的旅行时间函数的相关性，假设了一组基于真实数据的新基准实例。数值实验表明，使用与时间相关的旅行时间进行优化具有成本效益，但在计算上具有挑战性。因此，我们基于对最佳 TD-IRP 解决方案结构的观察，提出了一种分解问题的数学方法。所提出的数学方法首先定义要访问的客户集和每个时期要交付的数量，然后解决路由问题。数值实验证明它是非常有效的，并且产生的解决方案与找到的最佳下限有小的差距。因为它分离了路由问题，所提出的数学方法打开了通过利用关于时间相关路由问题的丰富文献非常有效地解决 TD-IRP 的可能性。