Provide solutions to the following numerical problems. Show work (otherwise point will be deducted).

1. An auto parts supplier sells Hardy-brand batteries to car dealers and auto mechanics. The annual demand is approximately 1,200 batteries. The supplier pays $28 for each battery and estimates that the annual holding cost is 30 percent of the batterys value. It costs approximately $20 to place an order (managerial and clerical costs). The supplier currently orders 100 batteries per month.

a. Determine the ordering, holding, and total inventory costs for the current order quantity.

b. Determine the economic order quantity ( EOQ ).

c. How many orders will be placed per year using the EOQ ?

d. Determine the ordering, holding, and total inventory costs for the EOQ. How has ordering cost changed? Holding cost? Total inventory cost?

2. Upon closer inspection, the supplier determines that the demand for batteries is normally distributed with mean 4 batteries per day and standard deviation 3 batteries per day. (The supplier is open 300 days per year.) It usually takes about 4 days to receive an order from the factory.

a. What is the standard deviation of usage during the lead time?

b. Determine the reorder point needed to achieve a service level of 95 percent.

c. What is the safety stock? What is the holding cost associated with this safety stock?

d. How would your analysis change if the service level changed to 99 percent?

3. Foster Drugs, Inc., handles a variety of health and beauty aid products. A particular hair conditioner product costs Foster $2.95 per unit. The annual holding cost rate is 20 percent. Using an EOQ model, they determined that an order quantity of 300 units should be used. The lead time to receive an order is one week, and the demand is normally distributed with a mean of 150 units per week and a standard deviation of 40 units per week.

a. What is the reorder point if the rm is willing to tolerate a 5-percent chance of a stockout during an order cycle?

b. What safety stock and annual safety stock cost are associated with your recommendation in part a ?

c. Foster is considering making a transition to a periodic-review system in an attempt to coordinate ordering of some of its products. The review period would be two weeks and the delivery lead time would remain one week. What target inventory level would be needed to ensure the same 5-percent risk of stockout?

d. What is the safety stock associated with your answer to part c ?

e. What is the annual cost associated with holding this safety stock?

f. Compare your answers to parts b and d . If you were the manager of Foster Drugs, would you choose a continuous- or periodic-review system?