Mixed Vendor/Retailer management of zero-cost multi-inventory systems

In this paper, an original mixed VMI (Vendor Management Inventory)/RMI (Retail Management Inventory) IRP (Inventory Routing Problem) characterized by zero inventory costs is considered, focusing on a quite typical scenario of multiproduct delivery to a network of retailers distributed over the territory. In this scenario, some retailers have the possibility to place orders on their own (pull retailers), while the orders of the other retailers (push retailers) are generated in automatic, through the original methodology here proposed. The objective is to avoid stock-outs, minimize transportation costs, and equalize the use of transportation resources over the considered planning horizon. The proposed MVRMIRP is formulated as a mixed-integer mathematical programming problem. Then, an original two-step algorithm is proposed, for solving the considered problem.