Im sorry, darling, Robert yells back. I have just discovered a way to control the inventory of a critical item at the drugstore. I am really excited because I am able to apply my industrial engineering degree to my job! I need to get the data from the store and work out the new inventory policy! I will be back before dinner! Because rush hour traffic has dissipated, the drive to the drugstore takes Robert no time at all. He unlocks the darkened store and heads directly to his office where he rummages through file cabinets to find demand and cost data for Totalee toothbrushes over the past year. Aha! Just as he suspected! 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 (30 days). 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 fulfills 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 20 miles from Nightingale Drugstore. The drugstore must now place orders with a warehouse located 350 miles away and must wait 6 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) Robert begins to wonder whether he would save money if he allows planned shortages to occur. Customers would wait to buy the toothbrushes from Nightingale since they have high brand loyalty and since Nightingale sells the toothbrushes for less. Even though customers would wait to purchase the Totalee toothbrush from Nightingale, they would become unhappy with the prospect of having to return to the store again for the product. Robert decides that he needs to place a dollar value on the negative ramifications from shortages. He knows that an employee would have to calm each disgruntled customer and track down the delivery date for a new shipment of Totalee toothbrushes. Robert also believes that customers would become upset with the inconvenience of shopping at Nightingale and would perhaps begin looking for another store providing better service. He estimates the costs of dealing with disgruntled customers and losing customer goodwill and future sales as $1.50 per unit short per year. Given the 6-day lead time and the shortage allowance, how many Totaleetoothbrushes should Robert order each time, and when should he order? What is the maximum shortage under this optimal inventory policy? What is the total variable inventory cost per year?

(d) Robert realizes that his estimate for the shortage cost is simply thatan estimate. He realizes that employees sometimes must spend several minutes with each customer who wishes to purchase a toothbrush when none is currently available. In addition, he realizes that the cost of losing customer goodwill and future sales could vary within a wide range. He estimates that the cost of dealing with disgruntled customers and losing customer goodwill and future sales could range from 85 cents to $25 per unit short per year. What effect would changing the estimate of the unit shortage cost have on the inventory policy and total variable inventory cost per year found in part (c)?

(e) Closing warehouses has not improved Totalees 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 6-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?