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.)

Question

Quizplus · Accepted Answer

The Answer is 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.

Located in Central France, Laurence Garreau's Firm Supplies a Particular