Problem 1. (Chapter 2: Logistics/Supply Chain Strategy and Planning) Describe the principle of differentiated distribution. Explain how it is illustrated in the following situations:

a. Total distribution costs are minimized if back orders on field warehouse inventories are filled from plant inventories. Premium transportation is used to ship back orders directly from plant to customers.

b. The product items stocked in a warehouse are grouped so that different stock availability levels are set for each of the groups.

c. All products are grouped according to an ABC classification scheme, where A items have high sales volume, B items have moderate sales volume, and C items have low sales volume. A items are stocked in field warehouses, B items are stocked in regional warehouses, and C items are stocked only at plant locations.

Problem 2. (Chapter 9: Inventory) Suppose that an auto part in a manufacturers inventory has the following characteristics:

Forecast of demand = 1,250 cases per week

Forecast error, std. dev. =475 cases per week

Lead time = 4 weeks

Carrying cost =30 % per year

Purchase price, delivered = $56 per case

Replenishment order cost =$40 per order

Stockout cost =$10 per case

Probability of being in stock during the lead time =80%

Assume the manufacturer uses ROP method to control the inventory of this item. a. What is the economic order quantity? b. Whats the standard deviation for the demand during lead time? Whats the safety stock? What is the reorder point? c. Whats the expected number of units out of stock annually? d. What is the annual service level? e. Whats the total annual costs excluding purchasing costs? f. If the lead time is normally distributed with a standard deviation of 0.5 weeks, whats the ROP?

Problem 3. (Chapter 9: Inventory) Cabot Appliances, a retail chain, is trying to decide what size order it should place with its supplier of room air conditioners. Room air conditioner sales are highly seasonal, and the number of units sold is very dependent on summer weather patterns. Carbot places one order per year. Reorders are impractical after the selling season begins to develop. Although the actual sales level cannot be known for sure, Cabot analyzes past selling seasons, long-term weather reports, and the general state of the economy. Cabot estimates that the demand for the air conditioner follows a normal distribution with a mean of 1000 and a standard deviation of 100. A unit has a delivered price to Carbot of $320 and it is priced to customers at $400. Air conditioners unsold at the end of the season are discounted to $300, which clears them from inventory. How many room air conditioners should Cabot order?