# 1. Buckeye Novelty Shop uses a continuous-review system and operates 52 weeks per year. One of the best-selling items has the following characteristics: Demand (D) = 14,000 units/year Ordering cost (S) = \$320/order Holding cost (H) = \$4/unit/year Lead time (L) = 3 weeks Cycle-service level = 95% Demand is normally distributed, with a standard deviation of weekly demand of 120 units. Current on-hand inventory is 1,308 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 95 units just occurred. Is it time to reorder? If so, how many should be ordered?

EOQ = Square root ( 2 x 320 x 14000/ 4) = 1497

Average time between orders = EOQ/annual demand x 52 weeks = 1497/14000 x 52 = 5.56 weeks

EOQ = 1497

AVERAGE TIME BETWEEN ORDERS = 5.56 WEEKS

Cycle service level =95 %

I.e. In stock probability = 0.95

Corresponding Z value = NORMSINV ( 0.95 ) = 1.6448

Standard deviation of demand during lead time

= Standard deviation of weekly demand x Square root ( Lead time of 3 days )

= 120 x Square root ( 3 )

= 120 x 1.732

= 207.84

Therefore , required safety stock

= Z value x standard deviation of demand during lead time

= 1.6448 x 207.84

= 341.85 ( 342 rounded to nearest whole number )

Reorder point = Average weekly demand x Lead time( weeks) + Safety stock

= (14000/52 ) x 3 + 342 = 807.69 + 342 = 1149.69 ( 1150 rounded to nearest whole number )

SAFETY STOCK = 342

REORDER POINT = 1150

Annual cost of placing order

= Co x D/ EOQ

= 320 X 14000/1497

= \$ 2992.65

Annual cost of holding the cycle inventory

= Ch x EOQ /2

= 4 X 1497/2

= \$2994

ANNUAL COST OF PLACING ORDER = \$2992.65

ANNUAL COST OF HOLDING CYCLE INVENTORY =\$2994

Current on hand inventory = 1308 units

Withdrawal quantity = 95 units

Net quantity post withdrawal = 1308 – 95 = 1213

Since net quantity post withdrawal ( i.e. 1213 ) > Reorder point 1150, IT IS NOT YET TIME TO REORDER

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