1. Suppose that Sam's Cat Hotel in Problem 10 uses a P system instead of a Q system. The average daily demand is 15 bags (90/6), and the standard deviation of daily demand is 6.124 bags (15√6).
a. What P (in working days) and T should be used to approximate the cost trade-offs of the EOQ?
b. How much more safety stock is needed than with a Q system?
c. It is time for the periodic review. How much kitty litter should be ordered?
2. Your firm uses a continuous review system and operates 52 weeks per year. One of the items handled has the following characteristics.
Demand (D) = 20,000 units/year
Ordering cost (S) = $40/order
Holding cost (H) = $2/unit/year
Lead time (L) = 2 weeks
Cycle-service level = 95%
Demand is normally distributed, with a standard deviation of weekly demand of 100 units.
Current on-hand inventory is 1,040 units, with no scheduled receipts and no backorders.
a. Calculate the item's EOQ. What is the average time, in weeks, between orders?
b. Find the safety stock and reorder point that provides a 95 percent cycle-service level.
c. For these policies, what are the annual costs of (i) holding the cycle inventory and (ii) placing orders?
d. A withdrawal of 15 units just occurred. Is it time to reorder? If so, how much should be ordered?
3. Suppose that your firm uses a periodic review system, but otherwise the data are the same as in Problem 2.
a. Calculate the P that gives approximately the same number of orders per year as the EOQ. Round your answer to the nearest week.
b. Find the safety stock and the target inventory level that provide a 95 percent cycle-service level.
c. How much larger is the safety stock than with a Q system?
4. A company begins a review of ordering policies for its continuous review system by checking the current policies for a sample of items. Following are the characteristics of one item.
Demand (D) = 64 units/week (Assume 52 weeks per year)
Ordering and setup cost (S) = $50/order
Holding cost (H) = $13/unit/year
Lead time (L) = 2 weeks
Standard deviation of weekly demand = 12 units
Cycle-service level = 88 percent
a. What is the EOQ for this item?
b. What is the desired safety stock?
c. What is the reorder point?
d. What are the cost implications if the current policy for this item is Q = 200 and R= 180?
5. Using the same information as in Problem 4, develop the best policies for a periodic review system.
a. What value of P gives the same approximate number of orders per year as the EOQ? Round to the nearest week.
b. What safety stock and target inventory level provide an 88 percent cycle-service level?
6. Wood County Hospital consumes 1,000 boxes of bandages per week. The price of bandages is $35 per box, and the hospital operates 52 weeks per year. The cost of processing an order is $15, and the cost of holding one box for a year is 15 percent of the value of the material.
a. The hospital orders bandages in lot sizes of 900 boxes. What extra cost does the hospital incur, which it could save by using the EOQ method?
b. Demand is normally distributed, with a standard deviation of weekly demand of 100 boxes. The lead time is 2 weeks. What safety stock is necessary if the hospital uses a continuous review system and a 97 percent cycle-service level is desired? What should be the reorder point?
c. If the hospital uses a periodic review system, with P = 2 weeks, what should be the target inventory level. I?
7. A golf specialty wholesaler operates 50 weeks per year. Management is trying to determine an inventory policy for its 1-irons, which have the following characteristics:
Demand (D) = 2,000 units/year
Demand is normally distributed
Standard deviation of weekly demand = 3 units
Ordering cost = $40/order
Annual holding cost (H) = $5/units
Desired cycle-service level = 90%
Lead time (L) = 4 weeks
a. If the company uses a periodic review system, what should P and T be? Round P to the nearest week.
b. If the company uses a continuous review system, what should R be?