Deck 4: Managing Flow Variability: Safety Inventory

Question 1

Located in central France, Laurence Garreau's firm supplies a particular subassembly to the automobile industry. The subassemblies are made in three different shapes (for different car models). These subassemblies need an electric motor, and Laurence is trying to find a supplier for these motors. The specifications of the electric motor required for the three subassemblies are almost identical; however the motors need to be of slightly different shapes to fit into the subassembly. Assume that the firm works for 300 days in a year and the daily requirement of each type of motor is normally distributed with a mean of 200 units and a standard deviation of 50 units. Laurence intends to hold safety stock to meet a 95% service level. The annual holding cost of the motor is 25% of the price of the motor. Also, by convention, the French firm pays for the motors the moment they are shipped.Laurence has received two quotations. The first is from a firm in Asia. The unit price per motor is 50 Euros. In addition, the transportation cost per unit is 5 Euros. The transit time from Asia is 25 days. The second quotation is from a company in North America. This firm offers to price the motors at 60 Euros/unit, and a transportation cost of 7.5 Euros. It will take only 10 days to deliver the motors.Evaluate each of the two proposals to determine the most economical alternative. What is your recommendation? (Be specific and show all of your calculations.)

Answer 1

Daily demand is normally distributed with mean = 200, and standard deviation = 50 For 95% service level, z=1.65
ASIA:
Unit cost, C=50 euros,
Holding cost per unit per year, H = 25% of C = 0.25 × 50 = 12.50 euros
Lead time (LT) = 25 days
Safety stock = z × std dev of demand during lead time = z × sqrt(LT) ×std dev of demand= 1.65 × sqrt(25) × 50 = 412.5
Since the French firm pays for the motors the moment they are shipped, we also need to consider holding costs for the pipeline stock.
With mean daily demand = 200 units, and lead time = 25 days,
Pipeline stock = 200×25 = 5,000 units
Total inventory = 412.5 + 5,000 = 5,412.5 units
Cost of holding inventory = 12.50 × 5,412.5 = 67,656.25 euros
Unit transportation cost = 5 euros
Total annual transportation cost = annual demand × unit transportation cost = 200 units/day × 300 days/year × 5 euros = 300,000 euros
Total cost of inventory holding and transportation = 300,000 + 67,656.25 = 367,656.25 euros
This is the cost for each type of motor. Since there are three slightly different types of motors being shipped, total cost = 3×367,656.25 = 1,102,968.75 euros
NORTH AMERICA
Unit cost, C=60 euros,
Holding cost per unit per year, H = 25% of C = 0.25× 60 = 15 euros
Lead time (LT) = 10 days
Safety stock = z × std dev of demand during lead time = z× sqrt(LT) ×std dev of demand = 1.65 × sqrt(10) × 50 = 260.88 units
Since the French firm pays for the motors the moment they are shipped, we also need to consider holding costs for the pipeline stock.
With mean daily demand = 200 units, and lead time = 10 days,
Pipeline stock = 200×10 = 2,000 units
Total inventory = 260.88 + 2,000 = 2,260.88 units
Cost of holding inventory = 15 × 2,260.88 = 33,913.20 euros
Unit transportation cost = 7.5 euros
Total annual transportation cost = annual demand × unit transportation cost = 200 units/day × 300 days/year × 7.5 euros = 450,000 euros
Total cost of inventory holding and transportation = 450,000 + 33,913.20 = 483,913.20 euros
This is the cost for each type of motor. Since there are three slightly different types of motors being shipped, total cost = 3×483,913.20 = 1,451,739.60 euros
So the North American firm's quote is more expensive. Go with the Asian firm.

Question 2

A fashion company decides to market denim jeans in unusual colors: lightning green, electric orange and shocking red. The company buys denim and dyes it in each of the three colors. The next step is producing the jeans - which involves cutting, sewing, etc. - in each of the three colors. In year 1, the company expected demand for each product to be approximately the same, and produced 100,000 units of each product. However, the electric orange jeans were a runaway success (demand was 250,000), while the other two colors sold only 25,000 units each. It is unclear which color will catch on next year, and the company wants to avoid facing the same problem. As a result they decide to reverse their operations, producing basic white denim jeans first, and then dyeing them in different colors. Assume that sufficient capacity exists in both operations, and the dyeing operation is a very simple and quick process. What specific advantages might the company derive from new "operations reversal" process? Does it help the company deal with the problem they faced last year?

Answer 2

Since the dyeing operation is simple and quick, the company can delay this step till better information is available - and still respond quickly to customer demand. In the current setup, the more complex and long operation (jean production) takes place after jeans have already been dyed in different colors, so it is harder to respond to demand fluctuations quickly. Thus, the company would have had to stock large amounts of inventory of each product (different colors) in order to protect itself from demand uncertainty. The "operations reversal" essentially delays differentiation of the product and improves the company's ability to respond fast to customer demand, and allows the company to pool their inventory (one basic type of jeans rather than multiple colors).

Question 3

Daily demand for the ice creams at I-Scream parlor is normally distributed with a mean of 160 quarts and a standard deviation of 100 quarts. The owner has the ice cream supplied by a wholesaler who charges $2 per quart. The wholesaler charges a $400 delivery charge independent of order size. It takes 4 days for an order to be supplied. The opportunity cost of capital to I-Scream is estimated to be 25% per year. Assume 360 days in the year. [Show all work]

-The optimal order size of each order is:

A) 13576 quarts
B) 9600 quarts
C) 6788 quarts
D) 716 quarts
E) 506 quarts

Answer 3

9600 quarts

Question 4

Daily demand for the ice creams at I-Scream parlor is normally distributed with a mean of 160 quarts and a standard deviation of 100 quarts. The owner has the ice cream supplied by a wholesaler who charges $2 per quart. The wholesaler charges a $400 delivery charge independent of order size. It takes 4 days for an order to be supplied. The opportunity cost of capital to I-Scream is estimated to be 25% per year. Assume 360 days in the year. [Show all work]

-The owner would like to ensure no stock-outs in 95% of the cycles. The optimal safety stock the store should have is:

A) 660 quarts
B) 528 quarts
C) 330 quarts
D) 264 quarts
E) 165 quarts

Question 5

Daily demand for the ice creams at I-Scream parlor is normally distributed with a mean of 160 quarts and a standard deviation of 100 quarts. The owner has the ice cream supplied by a wholesaler who charges $2 per quart. The wholesaler charges a $400 delivery charge independent of order size. It takes 4 days for an order to be supplied. The opportunity cost of capital to I-Scream is estimated to be 25% per year. Assume 360 days in the year. [Show all work]

-Currently the owner orders 4000 quarts of ice cream when they have 1680 quarts on hand. The average time spent by a quart of ice cream at the parlor is:

A) 39.6 days
B) 20 days
C) 19 days
D) 15 days
E) 12.5 days

Question 6

Two key components of Benetton's marketing strategy include (i) Higher variety than competition (ii) Lower price than competition. Clearly these components of their strategy are in conflict. List two operational actions that allow Benetton to support these objectives of the marketing strategy and execute them successfully.

Question 7

Big Old Tires currently owns and operates four warehouses in the Chicago area. Assume that each warehouse serves a geographic region. Weekly demands in any region are normally distributed with a mean of 200 tires and a standard deviation of 100 tires. Orders from suppliers take 4 weeks to be delivered. Big Old Tires is contemplating a consolidation of warehouses from four to one. Upon consolidation, the wholesaler carries the same safety stock in one warehouse as previously in four warehouses combined. The service level (in terms of probability of not stocking out in a cycle) s/he can provide from this single warehouse will be [Give 1-line explanation]:

A) Higher than before.
B) Same as before.
C) Lower than before.

Question 8

Hewlett-Packard produces deskjet printers for worldwide demand at its Vancouver, WA facility. It is observed that the monthly demand for type AB printers at the European DC averages 15,830 with a standard deviation of 5,624.

-The fixed cost of transportation and ordering is $100,000. Each printer costs $100 and HP has a holding cost of 20%. The optimal order quantity for the European DC is

A) About 43,585
B) About 12,582
C) About 125,817
D) About 435,844
E) None of the above

Question 9

Hewlett-Packard produces deskjet printers for worldwide demand at its Vancouver, WA facility. It is observed that the monthly demand for type AB printers at the European DC averages 15,830 with a standard deviation of 5,624.

-If the delivery lead time from the Vancouver factory is 6 months, how much safety stock of the AB printers should the European DC carry to provide a cycle service level (frequency of no stock-out) of 90%?

A) About 7,207
B) About 43,245
C) About 17,655
D) About 108,756
E) None of the above

Question 10

Hewlett-Packard produces deskjet printers for worldwide demand at its Vancouver, WA facility. It is observed that the monthly demand for type AB printers at the European DC averages 15,830 with a standard deviation of 5,624.
-HP is considering sending the printers by airfreight instead of sending them by sea. Airfreight will cost an extra $5 per printer but will reduce the delivery lead-time to 1 month. Identify the tradeoff that HP must consider when deciding whether to go with the airfreight option. What would you recommend? Why? Quantify the costs and benefits of the change.