A real-life Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet: Formulation and Adaptive Large Neighborhood Search based Matheuristic

•A new complex VRP arising in real distribution arising in real life.•An efficient Adaptive Large Neighborhood Search Matheuristic.•The large neighborhood is quickly and exhaustively explored directly with the model.•Extreme versatility and portability of the method. In this paper, a new rich Vehicle Routing Problem that could arise in a real life context is introduced and formalized: the Multi Depot Multi Period Vehicle Routing Problem with a Heterogeneous Fleet. The goal of the problem is to minimize the total delivery cost. A heterogeneous fleet composed of vehicles with different capacity, characteristics (i.e. refrigerated vehicles) and hourly costs is considered. A limit on the maximum route duration is imposed. Unlike what happens in classical multi-depot VRP, not every customer may/will be served by all the vehicles or from all the depots. The planning horizon, as in most real life applications, consists of multiple periods, and the period in which each route is performed is a variable of the problem. The set of periods, within the time horizon, in which the delivery may be carried out is known for each customer. A Mixed Integer Programming (MIP) formulation for MDMPVRPHF is presented in this paper, and an Adaptive Large Neighborhood Search (ALNS) based Matheuristic approach is proposed, in which different destroy operators are defined. Computational results, pertaining to realistic instances, which show the effectiveness of the proposed method, are provided.