On the Effectiveness of Direct Shipping Strategy for the One-Warehouse Multi-Retailer R-Systems

We consider the problem of integrating inventory control and vehicle routing into a cost-effective strategy for a distribution system consisting of one depot and many geographically dispersed retailers. All stock enters the system through the depot and is distributed to the retailers by vehicles of limited constant capacity. We assume that each one of the retailers faces a constant, retailer specific, demand rate and that inventory is charged only at the retailers but not at the depot. We provide a lower bound on the long run average cost over all inventory-routing strategies. We use this lower bound to show that the effectiveness of direct shipping over all inventory-routing strategies is at least 94% whenever the Economic Lot Size of each of the retailers is at least 71% of vehicle capacity. The effectiveness deteriorates as the Economic Lot Sizes become smaller. These results are important because they provide useful guidelines as to when to embark into the much more difficult task of finding cost-effective routes. Additional advantages of direct shipping are lower in-transit inventory and ease of coordination.