Charlotte O’Hara founded the Tara Cosmetic Company (TCC) in 1993 when she was a student at OU. Since then, TCC has become increasingly successful: gross revenues in 1994 exceeded $300,000. While preparing her 1994 tax retuns, Ms. O’Hara noticed that inventories had grown substantially -the 1994 inventory to sales ratio was about 6. TCC’s tax accountant pointed out that she would require a substantial bank loan if inventory growth persisted Wilsons’s close friend Brett was a junior at OU. Having taken POM 343, he offered to help analyze the inventory situation in return for tickets to the upcoming Pistons game against Atlanta. After a lengthy discussion, Charlotte and Brett agreed that a thorough analysis of one particular item -half-ounce bottles of “Red Earth Musk” – – would provide an excellent indication of cost savings to be achieved through changes in ordering and inventory practices. Brett spent a weekend rummaging through boxes full of company records, invoices and sales slips to get as much data as possible about “Red Earth Musk.” He found that demand for this cologne averaged 35 bottles per week over the last two years with a weekly mean absolute deviation of 7 bottles. TCC’s purchase price was $8 per half- ounce bottle, packaged and ready to sell. During these two years, the ordering policy has been to order 35 bottles each week. The supplier has always delivered these bottles exactly two weeks after the order was placed. Charlotte and Brett met with the accountant and figured out that the cost to TCC for placing an order was $2.50. The cost of holding a bottle in inventory for a year was difficult to assess, but all agreed that the yearly taxes, insurance and storage costs of a bottle of “Red Earth Musk” was 75 cents. They further estimated the cost of capital at 12% per year. TCC is open 5 days a week (Tuesday-Saturday), 48 weeks each year A. What is the total annual cost of the current ordering policy of 35 bottles of “Red Earth Musk” each week? What is the order quantity and the total annual savings if TCC were to adopt an ordering policy based on an economic order quantity? B. C. If TCC were to set up a continuous review system with a 5% chance of not fulfilling demand from stock (z on hand? 1.65), how many bottles of safety stock should they keep Develop a periodic inventory control system for TCC for their “Red Earth Musk.” Use z 2.05. State the appropriate decision rule. D.

## Expert Answer

d Demand 35 units Per week

D Demand annually 1680 units Annually (@48 weeks) Z Z value 2.05

p Purchase cost 8 $ per unit R So reorder point 91 (LTD+SLTD *Z) Ans D

K Ordering cost 2.5 $ per order EOQ (Sqrt(2*k*D/h) 93.54143467 units Ans D

h Holding cost 0.96 $ per unit (Cost of capital 12%) SS Safety stock 21 (R-LTD) Ans D

LT Lead time 2 Weeks AI Average inventory 92.27071733 units (EOQ+R)/2 Ans D

Working days 240 Days (AI*h) Holding cost 88.57988864 $

Sigma Std Dev of annual demand 48.49742261 SQRT((weekly std dev^2)*Weeks) N No of orders 17.95995546 times

LTD Lead time demand 70 Units Q 35 Units

SLTD Std Dev for lead time 9.899494937 units N 48 Times

P value for 1 stock out, 95% Toc Total ordering cost annualy 120 $

Z Z value 1.65 Thc Annual Holding cost 16.8 $

R So reorder point 87 (LTD+SLTD *Z) Tpc Purchasing cost annual 13440 $

EOQ (Sqrt(2*k*D/h) 93.54143467 units Ans B TC Total cost 13576.8 $ Ans A

SS Safety stock 17 (R-LTD) Ans C

AI Average inventory 90.27071733 units (EOQ+R)/2

(AI*h) Holding cost 86.65988864 $ Q 150 Units

N No of orders 17.95995546 times N 11.2 Times

Toc Total ordering cost annualy 44.89988864 $ Total orders/EOQ Toc Total ordering cost annualy 28 $

Thc Annual Holding cost 86.65988864 $ Thc Annual Holding cost 72 $

Tpc Purchasing cost annual 13440 $ Tpc Purchasing cost annual 13020 $ (1680 @7.75)

TC Total cost 13571.55978 $ (Toc+Thc+Tpc) Ans B TC Total cost 13120 $ Ans E

Length of order cycle 13.3630621 days (Total days/No of orders)

So, the discount offer should be taken as: Total savings = 456.8 from current policy and $451.6 more saving from EOQ.