A vendor managed inventory model using continuous approximations for route length estimates and Markov chain modeling for cost estimates

We consider a vendor who supplies goods to a set of geographically dispersed retailers and can monitor and control the inventory levels at the retailers. Such an arrangement is often called vendor managed inventory (VMI). The decisions in this set-up are the inventory levels at the warehouse and at the retailers and the routing along the retailers. Normally, the inventory levels at the vendor’s warehouse and at the retailers are established by modeling the problem as a joint replenishment problem (JRP). Such a model ignores the differences in distances, number of retailers visited, and vehicle loads that may occur, in particular when these retailers are served on joint delivery trips. Some approaches that take routing and inventory decisions into account jointly, but these are so complex that only relatively small instances can be solved.