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 1.65), how many bottles of safety stock should they keep demand from stock ( z on hand? Develop a periodic inventory control system for TCC for their “Red Earth Musk.” Use z D. 2.05. State the appropriate decision rule.

## 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.