Question

Sam's Cat Hotel operates 5252 weeks per? year, 77 days per? week, and uses a continuous review inventory system. It purchases kitty litter for ?$10.7510.75 per bag. The following information is available about these bags. Refer to the standard normal table LOADING... for? z-values.

Demand = 100 bags/weeks

Order cost = $56/order

Annual Holding Cost = 30 percent of cost

Desired cycle-service level =99 percent Lead time = 2 weeks (14 working days)

Standard deviation of weekly demand = 10 bags

Current on-hand inventory is 315 bags with no open orders or backorders

d. The store currently uses a lot size of 495 bags (i.e, Q =495).

What is the annual holding cost of this policy? The annual holding cost is ??? (Enter your response and round to two decimal places)

What is the annual ordering cost? The annual ordering cost is ??? (Enter your respone and round to two decimal places)

Without calculating the EOQ, how can you conclude from these two calucations that the current lot size is too large? Select the correct answer from the multiple choice below.

A. When Q= 495, the annual holding cost is larger than the ordering cost, therefore Q is too large.

B. There is not enough information to determine this.

C. When Q=495, the annual holding cost is less then the ordering cost, therefore Q is too small.

D. Both quantiies are appropriate.

Please answer the following questions for section e.

e. What would be the annual cost saved by shifting from the 495 bag lot size to the EOQ?

The annual holding cost with the EOQ is ??? (Enter your response rounded to two decimal places)

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

Therefore, Sam's Cat Hotel saves ??? by shifting from the 495 bag lot size to the EOQ? (Enter your response rounded to the nearest two decimal places)

Answer 1

For Q = 495 :

Annual holding cost

= Annual unit inventory holding cost x Q/2

= 30% of $10.75 x 495/2

= $3.225 X 495/2

= $798.19 ( rounded to 2 decimal places )

Annual ordering cost

= Ordering cost x Number of orders

= $56 x Annual demand / Q

= $56 x 5200 /495

= $588.28

Total annual ordering cost plus annual holding cost = $798.19 + $588.28 = $1386.47

At EOQ , Annual ordering cost = Annual inventory holding cost

Annual ordering cost = Ordering cost x annual demand / order quantity

Annual inventory holding cost = Annual unit inventory cost x Order quantity /2

Thus when order quantity increase from EOQ level :

Annual inventory holding cost increases since “order quantity “ appears in numerator

Annual ordering cost reduces sine “order quantity” appears in numerator

In the given case ,

Annual holding cost $798.19 > Annual ordering cost of $588.28

Therefore , Q is too large

ANSWER : A) WHEN Q= 495, THE ANNUAL HOLDING COST IS LARGER THAN ANNUAL ORDERING COST, THEREFORE Q IS TOO LARGE

Answer to question e :

Annual demand = D = 100 bags/ week x 52 weeks = 5200 weeks

Order cost = Co = $56 / order

Annual unit holding cost = Ch = 30% of $10.75 = $3.225

Economic order quantity ( EOQ )

= Square root ( 2 x Co x D / Ch )

= Square root ( 2 x 56 x 5200 / 3.225)

= 424.95 ( 425 rounded to nearest whole number )

Annual ordering cost = Order cost x Number of orders= Co x annual demand/order quantity = $56 x 5200/425 = $685.18 ( rounded to 2 decimal places)

Annual inventory holding cost = Annual unit holding cost x Average inventory = Ch x EOQ/2 = $3.225 x 425/2 = $685.31

Total annual ordering cost plus holding cost = $685.18 + $685.31 =$1370.49

Amount Sam’s cat hotel saves

= Total annual ordering plus holding cost for EOQ – Total annual ordering plus holding cost for Q = 495

= $1386.47 - $1370.49

= $15.98