# What is Vendor Managed Inventory (VMI)? Why do companies use this technique?

MAN 5501 EXAM

PRODUCTION AND OPERATIONS MANAGEMENT

PROFESSOR JANICE E. CARRILLO

Instructions:

a. The exam format is open book, open note.

b. You must show all of your calculations either by writing them on the exam and scanning the file, or by saving them in separate Excel file. Please upload all files to the course website at the end of the exam, and include your last name in the file names.

c. Within the file, create a different worksheet for each individual problem, and label each worksheet with the problem number.

d. The first 6 question are worth 15 points each, and the last 7thquestion is worth only 10 points.

TOTAL_____________/100 2

1. The Oka-B shoe e-tailer has one person who answers the incoming telephone calls for the online store. Currently, the store receives an average of one call every 4 minutes, with a standard deviation in this interarrival time of 4 minutes (assume a Poisson arrival process). The phone operator answering the phone requires an average of 3 minutes to handle a call. The standard deviation in this activity time is 1 minute. Assume that if the phone operator is busy, that customers will wait on hold until the phone operator is available.

a. If the clerk works for 8 hours a shift, how much idle time will she have during a shift? (5 points)

b. What is the average total cost of the telephone lines over an 8-hour shift. Assume that the telephone company charges \$5.00 per hour for the telephone lines whenever they are in use (either being helped or waiting). Also, assume that the telephone operator earns \$10/hour. (5 points)

c. Should Oka-B hire a second person to help answer the calls? Justify your answer with the appropriate calculations. (5 points)

2. The manager of a large group of employees must decide whether she needs another photocopying machine. The cost of a machine is \$40 per 8 hour day regardless of whether the machine is in use. On average, 4 people need to use the copying machine per hour. Each person uses the copier for an average of 10 minutes. Interarrival times and copying times are exponentially distributed. Employees are paid \$8 per hour and we assume that a waiting cost is incurred when a worker is waiting in line or is using the copying machine.

a. What type of queuing system best describes this problem? (3 points)

b. What are the mean interarrival and service times? (4 points)

c. Calculate the average waiting time in line that each worker incurs. (4 points)

d. How many copying machines should be rented? (4 points)

3. A window installation company installs about 1000 windows per year, 18% of which are high end windows. All of the high end windows are purchased from a single international supplier at a cost of \$18.50 each. The installation company uses a holding cost based on a 25 percent annual interest rate. The setup cost for placing an order is estimated to be \$30.

a. How many high-end windows should the installation company order? (4 points)

b. How many orders should the installation company place each year? (3 points)

c. What is the total annual cost (including inventory related and materials cost) for the firm? (4 points)

d. If the supplier offers a quantity discount such that the installation firm only has to pay \$17.00 per high end window for ordering in batches of least 75 units, should they take advantage of this discount? (4 points) 3

4. A local coffee shop uses 50 bags of whole bean coffee every month, and you may assume that demand is perfectly steady throughout the year. The coffee shop has signed a year-long contract to purchase its coffee from a local supplier, Sweetwater coffee, for a price of \$25 per bag and an \$85 fixed cost for every delivery independent of the order size. The holding cost due to storage is \$1 per bag per month. The coffee shop managers figure their cost of capital is approximately 2% per month.

a. What is the optimal order size, in bags? (3 points)

b. Given your answer in (a), how many times a year does the coffee shop place orders? (3 points)

c. Given your answer in (a), how many months of supply of coffee does the coffee shop have on average? (3 points)

d. On average, how many dollars per month does the coffee shop spend to hold coffee (including the cost of capital)? (3 points)

e. Assume that Sweetwater is willing to give a 5 % (all-units) quantity discount if the buyer orders 100 bags or more at a time. If the coffee shop is interested in minimizing its total costs (i.e. purchase and inventory-related costs), should the coffee shop begin ordering 100 or more cases at a time? (3 points)

5. The local sporting goods store is trying to decide how many snow caps to stock during the winter season. Based on data from the past few seasons, the manager determines that past demand has been normally distributed with a mean of 350 and a standard deviation of 100. Each cap is fairly expensive, and sells for \$35 in the peak season. The sporting good store purchases these caps from a local vendor for \$10 a cap. At the end of the season, the remaining caps can be sold at a local swap meet for \$5 a cap.

a. What is the critical ratio? (4 points)

b. How many caps should the manager purchase? (4 points)

c. Suppose the manager stocks 400 of the caps. What’s the probability of a stock-out? (3 points)

d. For a ski parka item, it is optimal for the manager to stock 152 of them. What is the critical ratio, given that the mean sales are 100, and the standard deviation is 50 for the parkas? Assume that demand is normally distributed. (4 points)

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6. Samantha Wang is opening a new wine store. She is trying to decide how many bottles of a particular type of wine to stock in her new store. Samantha has collected some pricing and cost data to help her decide how many bottles of the wine to order for a particular type of wine. She estimates that the selling price is \$40.00 and the cost is \$19.80 for each bottle. Samantha predicts total demand for the wine to be normally distributed with mean of 980 and standard deviation of 354. Left over bottles will be given to the local charity for no cost. (15 points)

a. What is the critical ratio? (3 points)

b. How bottles of wine should Samantha purchase? (4 points)

c. Suppose 1200 bottles of wine are ordered and available for sale. What is the in-stock probability? (4 points)

d. Samantha’s co-owner (her husband) would like to strive for at least a 95% in stock probability. How many bottles of wine should she order for this? (4 points)

7. Answer the following questions:

a. For a single server queuing system, what happens when the mean arrival rate is equal to the mean service rate? (3 points)

b. In the Wall Street Journal article on “Bullwhip Hits Firms as Growth Snaps Back,” why are companies experiencing bullwhip effect? What are the key factors driving the inventory turnaround? What techniques is Caterpillar using to deal with these problems? (3 points)

c. What is Vendor Managed Inventory (VMI)? Why do companies use this technique? (4 points)

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