Brushing up on Inventory Control

Robert Gates rounds the corner of the street and smiles when he sees his wife pruning rose bushes in their front yard. He slowly pulls his car into the driveway, turns off the engine, and falls into his wife's open arms. "How was your day?" she asks. "Great! The drugstore business could not be better!" Robert replies. "Except for the traffic coming home from work! That traffic can drive a sane man crazy! I am so tense right now. I think I will go inside and make myself a relaxing martini." Robert enters the house and walks directly into the kitchen. He sees the mail on the kitchen counter and begins flipping through the various bills and advertisements until he comes across the new issue of OR/MS Today. He prepares his drink, grabs the magazine, treads into the living room, and settles comfortably into his recliner. He has all that he wants -except for one thing. He sees the remote control lying on the top of the television. He sets his drink and magazine on the coffee table and reaches for the remote control. Now, with the remote control in one hand, the magazine in the other, and the drink on the table near him, Robert is finally the master of his domain. Robert turns on the television and flips the channels until he finds the local news. He then opens the magazine and begins reading an article about scientific inventory management. Occasionally he glances at the television to learn the latest in business, weather, and sports. As Robert delves deeper into the article, he becomes distracted by a commercial on television about toothbrushes. His pulse quickens slightly in fear because the commercial for Totalee toothbrushes reminds him of the dentist. The commercial concludes that the customer should buy a Totalee toothbrush because the toothbrush is Totalee revolutionary and Totalee effective. It certainly is effective; it is the most popular toothbrush on the market!

At that moment, with the inventory article and the toothbrush commercial fresh in his mind, Robert experiences a flash of brilliance. He knows how to control the inventory of Totalee toothbrushes at Nightingale Drugstore! As the inventory control manager at Nightingale Drugstore, Robert 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. Robert now knows a way to prevent the inventory problems through scientific inventory management! He grabs his coat and car keys and rushes out of the house. As he runs to the car, his wife yells, "Honey, where are you going?" "I'm 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 management science 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. 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 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) 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. He estimates that an employee would spend an average of 5 minutes with each customer who wishes to purchase a toothbrush when none are currently available, and Nightingale employees are currently paid $8.40 per hour. 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 losing customer goodwill and future sales as $1.50 per unit short per year. Given the five-day lead time and the shortage allowance, how many Totalee toothbrushes 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 that - an estimate. He realizes that employees could spend an average of anywhere from 3 minutes to 10 minutes with each customer who wishes to purchase a toothbrush when none are currently available. He also realizes that the cost of losing customer goodwill and future sales could range from $0 to $20 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 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?