Inventory Routing in Practice

PRAXAIR (www.praxair.com) is a large industrial gases company with about 60 production facilities and over 10,000 customers across North America. PRAXAIR recently negotiated a policy with its customers in which PRAXAIR is in charge of managing its customers’ inventories. Customers will no longer be calling PRAXAIR to request a delivery. Instead, PRAXAIR will determine who receives a delivery each day and what the size of that delivery will be. PRAXAIR will use gauge readings received from remote telemetry units as well as regular customer phone calls to monitor and forecast product inventories. The distribution planning problems associated with such vendor managed resupply policies are known as inventory routing problems. Inventory routing problems are very different from vehicle routing problems. Vehicle routing problems occur when customers place orders and the delivery company, on any given day, assigns the orders for that day to routes for trucks. In inventory routing problems, the delivery company, not the customer, decides how much to deliver to which customers each day. There are no customer orders. Instead, the delivery company operates under the restriction that its customers are not allowed to run out of product. Another difference is the planning horizon. Vehicle routing problems typically deal with a single day, with the only requirement being that all orders have to be delivered by the end of the day. Inventory routing problems deal with a longer horizon. Each day the delivery company makes decisions about which customers to visit and how much to deliver to each of them, while keeping in mind that decisions made today impact what has to be done in the future. The objective is to minimize the total cost over the planning horizon while making sure no customers run out of product. The flexibility to decide when customers receive a delivery and how large these deliveries will be may significantly reduce distribution costs. However, this flexibility also makes it very difficult to determine a good, much less an optimal, cost effective distribution plan. When the choice becomes which of the customers to serve each day (PRAXAIR has over 10,000 customers) and how much to deliver to them, the choices become virtually endless. Vendor managed resupply policies can be used in many situations. In some instances, the use of such a policy is natural, such as when the “customers” are