Question

Sam's Cat Hotel operates 52 weeks per? year, 5 days per? week, and uses a continuous review inventory system. It purchases kitty litter for ?$11.50 per bag. The following information is available about these bags. Refer to the standard normal table LOADING... for? z-values.

Demand ?= 80 ?bags/week

Order cost? = ?$58?/order

Annual holding cost? = 30 percent of cost

Desired ?cycle-service levelequals90 percent

Lead time? = 2 ?week(s) ?(10 working? days)

Standard deviation of weekly demand? = 16 bags

Current ?on-hand inventory is 310 ?bags, with no open orders or backorders.

a. What is the? EOQ?

?Sam's optimal order quantity is

374 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

nothing weeks. ?(Enter your response rounded to one decimal? place.)

b. What should R ?be?

The reorder point is

nothing 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?

d. The store currently uses a lot size of 505 bags? (i.e., Qequals505?). What is the annual holding cost of this? policy?

The annual holding cost is ?$

nothing. ?(Enter your response rounded to two decimal? places.)

What is the annual ordering? cost?

The annual ordering cost is ?$

nothing. ?(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. When Q? = 505?, the annual holding cost is larger than the ordering? cost, therefore Q is too large.

B. Both quantities are appropriate.

C. There is not enough information to determine this.

D. When Q? = 505?, the annual holding cost is less then the ordering? cost, therefore Q is too small.

E. What would be the annual cost saved by shifting from the 505?-bag lot size to the? EOQ?

The annual holding cost with the EOQ is ?$

nothing. ?(Enter your response rounded to two decimal? places.)

The annual ordering cost with the EOQ is ?$

nothing. ?(Enter your response rounded to two decimal? places.)

?Therefore, Sam's Cat Hotel saves ?$

nothing by shifting from the 505?-bag lot size to the EOQ. ?(Enter your response rounded to two decimal? places.)

Answer 1

As per policy only first four questions will be answered

Part A

Economic order quantity

d= 80 bags/week

D = 52*80 =4160

S= 58

Price = 11.50

H = 30%*11.50 = 3.45

EOQ = sqrt (2*D*S/ H) = (2*4160*58 / 3.45)^(1/2) = 374 bags

The average time between orders, in weeks

Q/D = 374/4160 = 0.08990 years = 4.45 weeks

Part B

Reorder point, R

R = demand during protection interval + safety stock

Demand during protection interval = dL = 80*2 = 160 bags

Safety stock

When the desired cycle-service level is 90%, z= 0.90

SD(L) = SD(t) *L^0.5 = 16*(2^0.5) = 22.63 = 23

Safety stock = 0.90* 23 = 20.7 or about 21 bags

R = 160+21 =181 bags

Part C

Initial inventory position = OH + SR BO = 310+0-0=310-10=300

Because inventory position remains above 181, it is not yet time to place an order.

Part D

Annual holding cost = Q/2*H = 505/2*30%*11.50 = 871.13

Annual ordering cost = D/Q*S =4160/505*58=477.78

Total cost = 871.13+477.78= 1348.91

At the EOQ, these two costs are equal. When , the annual holding cost is larger than the ordering cost, therefore Q is too large. (answer is option A)