Case 1: Brushing Up on Inventory (30%) ?As the inventory control manager at Nightingale Drugstore, Robert Gates has been experiencing problems keeping Totalee toothbrushes in stock. He has discovered that customers are very loyal to the Totalee brand name since Totalee holds a patent on the toothbrush endorsed by nine out of 10 dentists. Customers are willing to wait for the toothbrushes to arrive at Nightingale Drugstore since the drugstore sells the toothbrushes for twenty percent less than other local stores. This demand for the toothbrushes at Nightingale means that the drugstore is often out of Totalee?toothbrushes. The store is able to receive a shipment of toothbrushes several hours after an order is placed to the Totalee regional warehouse because the warehouse is only twenty miles away from the store. Nevertheless, the current ?inventory situation causes problems because numerous emergency orders cost the store unnecessary time and paperwork and because customers become disgruntled when they must return to the store later in the day.

The demand data for the toothbrushes is almost constant across the months. Whether in winter or summer, customers have teeth to brush, and they need toothbrushes. Since a toothbrush will wear out after a few months of use, customers will always return to buy another toothbrush. The demand data shows that Nightingale Drugstore customers purchase an average of 250 Totalee toothbrushes per month.
After examining the demand data, Robert investigates the cost data. Because Nightingale Drugstore is such a good customer, Totalee charges its lowest wholesale price of only $1.25 per toothbrush. Robert spends about 20 minutes to place each order with Totalee. His salary and benefits add up to $18.75 per hour. The annual holding cost for the inventory is 12 percent of the capital tied up in the inventory of Totalee toothbrushes.

(a) Robert decides to create an inventory policy that normally fulfils all demand since he believes that stock-outs are just not worth the hassle of calming customers or the risk of losing future business. He therefore does not allow any planned shortages. Since Nightingale Drugstore receives an order several hours after it is placed, Robert makes the simplifying assumption that delivery is instantaneous. What is the optimal inventory policy under these conditions? How many Totalee toothbrushes should Robert order each time and how frequently? What is the total variable inventory cost per year with this policy?

(b) Totalee has been experiencing financial problems because the company has lost money trying to branch into producing other personal hygiene products, such as hairbrushes and dental floss. The company has therefore decided to close the warehouse located twenty miles from Nightingale Drugstore. The drugstore must now place orders with a warehouse located 350 miles away and must wait five days after it places an order to receive the shipment. Given this new lead time, how many Totalee toothbrushes should Robert order each time, and when should he order?

(c) Closing warehouses has not improved Totalee's bottom line significantly, so the company has decided to institute a discount policy to encourage more sales. Totalee will charge $1.25 per toothbrush for any order of up to 500 toothbrushes, $1.15 per toothbrush for orders of more than 500 but less than 1000 toothbrushes, and $1 per toothbrush for orders of 1000 toothbrushes or more. Robert still assumes a five-day lead time, but he does not want planned shortages to occur. Under the new discount policy, how many Totalee toothbrushes should Robert order each time, and when should he order? What is the total inventory cost (including purchase costs) per year?

Case 2: Delivery System Design at Bullseye Department Store

Bullseye Department store is a discount retailer of general mechandise. The company owns 50 stores, but they are supplied from a single warehouse. Most of the mechandise received at the warehouse arrives in trucks.

Trucks arrive at the warehouse at random with a rate of once every seven minutes on average. Eight loading docks are available at the warehouse. A single worker mans each dock and is able to unload a truck in approximately 30 minutes on average. When all the docks are occupied, arriving trucks wait in a queue until one becomes available.

Bullseye has received complaints from some of the trucking firms that deliveries are taking too long at the warehouse. In response, Bullseye is considering a number of options to try to reduce the time trucks must spend at the warehouse. One option is to hire an extra worker for each of the loading docks. This is expected to reduce the average time it takes to unload a truck to eighteen minutes. It costs approximately £17 per hour in salary and fringe benefits to employ each additional worker.

Alternatively, the company can continue to use a single worker at each loading dock but upgrade the forklift equipment workers use to unload trucks. The company can replace the existing forklift equipment with a new model that can be leased for £6 per hour and is expected to reduce the average time required to unload a truck to 23 minutes.

Finally, the company can build two new loading docks for a capitalized cost of £6 per hour and hire two additional workers at a rate of £17 per hour to man these locations. Bullseye estimates its costs of £60 in goodwill for each hour a truck spends at the warehouse.

Which, if any, of the three alternatives Bullseye should implement?