Question

Sam's Cat Hotel operates 52 weeks per year, 7 days per week, and uses a continuous review inventory system. It purchases kitty litter for $10.75 per bag. The following information is available about these bags. Refer to the standard normal table for z-values. 

>Demand 95 bags/week 

>Order cost $56/order 

>Annual holding cost = 30 percent of cost 

>Desired cycle-service level = 99 percent 

>Lead time = 4 week(s) (28 working days) 

>Standard deviation of weekly demand = 20 bags 

>Current on-hand inventory is 325 bags, with no open orders or backorders

a. What is the EOQ? 

Sam's optimal order quantity is _______  bags. (Enter your response rounded to the nearest whole number.) 

What would be the average time between orders (in weeks)? 

The average time between orders is _______  weeks. (Enter your response rounded to one decimal place.) 

b. What should R be? The reorder point is 118 bags. (Enter your response rounded to the nearest whole number.) 

c. An inventory withdrawal of 10 bags was just made. Is it time to reorder? 

It is not time to reorder. 

d. The store currently uses a lot size of 490 bags (i.e., Q 490). What is the annual holding cost of this policy? 

The annual holding cost is $ 817.08. (Enter your response rounded to two decimal places.) 

What is the annual ordering cost? 

The annual ordering cost is $ 615.51. (Enter your response rounded to two decimal places.) 

Without calculating the EOQ, how can you conclude from these two calculations that the current lot size is too large? 

 A. There is not enough information to determine this.

 B. When Q 490, the annual holding cost is less then the ordering cost, therefore Q is too small.

 C. When Q 490, the annual holding cost is larger than the ordering cost, therefore Q is too large. 

 D. Both quantities are appropriate 

e. What would be the annual cost saved by shifting from the 490-bag lot size to the EOQ? 

The annual holding cost with the EoQ is S 708.69. (Enter your response rounded to two decimal places.) 

The annual ordering cost with the EOQ is $ 709.65. (Enter your response rounded to two decimal places.) 

Therefore, Sam's Cat Hotel saves $ 14.25 by shifting from the 490-bag lot size to the EOQ. (Enter your response rounded to two decimal places.)

Answer 1

A.

EOQ = (2*52*95*56/(.3*10.75))^.5

EOQ = 414.2 or 414 bags

Average time between the orders = 52/(52*95/414) = 4.4 weeks

B.

At 99%, value of Z = 2.33

Reorder point with safety stock = LT*D + Z*SD*LT^.5 = 4*95 + 2.33*20*4^.5

Reorder point with safety stock = 473.2 or 473 bag

Reorder point without safety stock = 4*95 = 380 bag

C.

Yes, its time to reorder

D.

Annual holding cost = (490/2)*(30%*10.75) = $790.13

Annual ordering cost = (52*95/490)*56 = $564.57

E.

Annual holding cost with EOQ = (414/2)*(30%*10.75) = $667.58

Annual ordering cost with EOQ = (52*95/414)*56 = $668.21

Savings = (790.13+564.57) - (667.58 +668.21)

Savings = $18.91