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.
(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 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 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 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 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?