Reducing environmental impact, related regulations and potential for operational benets are the main reasons why companies share their returnable transport items (RTIs) among the dierent partners of a closed-loop supply chain. In this paper, we consider a producer, located at a depot, who has to distribute his products packed in RTIs to a set of customers. Customers dene a time window wherein the service can begin. The producer is also in charge of the collection of empty RTIs for reuse in the next production cycle. Each partner has a storage area composed of both empty and loaded RTI stock, as characterized by initial levels and maximum storage capacity. As deliveries and returns are performed by a homogeneous eet of vehicles that can carry simultaneously empty and loaded RTIs, this research addresses a pickup and delivery inventory-routing problem within time windows (PDIRPTW) over a planning horizon.A mixed-integer linear program is developed and tested on small-scale instances. To handle more realistic large-scale problems, a cluster rst-route second matheuristic is proposed.
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