The Inventory Routing Problem (IRP) has been highlighted as a valuable strategy for tackling routing and inventory problems. This paper addresses the IRP but considers the forward delivery and the use of Returnable Transport Items (RTIs) in the distribution strategy. We develop an optimization model by considering inventory routing decisions with RTIs collection (backhaul customers) of a Closed-Loop Supply Chain (CLSC) within a short-term planning horizon. RTIs consider reusable packing materials such as trays, pallets, recyclable boxes, or crates. The RTIs represent an essential asset for many industries worldwide. The solution of the model allows concluding that if RTIs are considered for the distribution process, the relationship between the inventory handling costs of both the final goods and RTIs highly determines the overall performance of the logistics system under study. The obtained results show the efficiency of the proposed optimization scheme for solving the combined IRP with RTIs, which could be applied to different real industrial cases.

In this paper, we introduce an inventory routing problem with network disruptions. In this problem, not only decisions on inventory levels and vehicle routing are made simultaneously, but also, we consider disruptions over the networks in which a number of arcs are vulnerable to these disruptions, leading to an increase in travel times. We develop a dynamic programming approach to deal with this situation, and we also evaluate some policies adapting well-known instances from the literature.

We study an inventory routing problem (IRP) for the restaurant chain. We proposed a model a multi-product multi-vehicle IRP (MMIRP) with multi-compatibility and site-dependency (MMIRP-MCSD). The problem was formulated as a mixed integer programming (MIP). This model is difficult to solve because it is a problem that integrates MMIRP, a multi-compartment vehicle routing problem (MCVRP), and a site dependent VRP (SDVRP), each of which is difficult even by itself. Therefore, in this study, we proposed three-stage Math Heuristics based on the cluster-first and route-second method. In the numerical experiment, verification was performed using actual data, and knowledge on the decision making of the optimum vehicle type was obtained.