Problem 2

 

3. The warehouse store in Problem #2 has a lot of market power. It has convinced its supplier to build a warehouse nearby and to provide vendor-managed-inventory (VMI) services-including delivery-- for free, with inventory being delivered on consignment. Under a vendor-managed inventory system, the warehouse store no longer sends orders to the supplier. Instead the supplier is responsible for managing the inventory according to some rules that are mutually agreed upon by the buyer and supplier. Under a consignment system, the buyer does not pay the supplier for the goods until the buyer has sold the product. Thus, the supplier owns the inventory and incurs the financial cost of holding it until it is sold. It costs approximately $50 for the supplier to make a delivery, and $6.00 for the supplier to manufacture a package of paper towels. The supplier uses an annual inventory holding cost rate of 80%. The supplier plans to (electronically) check the inventory status at the warehouse store at the end of each day, and expects to be able to make a delivery by the end of the following day. The warehouse store has asked for a 98% probability of no stockout during the order cycle, but the supplier also recognizes that each shortage will result in a lost sale, and it will therefore lose its profit if a shortage occurs. For simplicity, you may assume that a year has 50 weeks, and each week has 7 wrking days. (That is, deliveries can be made on any day of the week.) (a) How often should the supplier send a truck to the warehouse store? (b) Use the Newsvendor model to estimate the economically optimal probability of no stockout during the order cycle.