An assign-and-route matheuristic for the time-dependent Inventory Routing Problem
Résumé
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.