Sam\'s Cat Hotel operates 52 weeks per year, 5 days per week, and uses a continu
ID: 369738 • Letter: S
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 $12.00 per bag. The following information is available about these bags.
Demand = 96 bags/week
Order cost = $56/order
Annual holding cost = 26 percent of cost
Desired cycle-service level=99 percent
Lead time = 4 week(s) (20 working days)
Standard deviation of weekly demand = 16 bags
Current on-hand inventory is 350 bags, with no open orders or backorders.
A.What is the EOQ?
sams optimal order quantity is ____ bags (Enter your response rounded to the nearest whole number.)
The average time between orders is ____ weeks. your response rounded to one decimal place.)
B. What should R be?
The reorder point is ____ 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/is not time to reorder. (Pick one)
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 $______ (Enter your response rounded to two decimal places.)
What is the annual ordering cost?
The annual ordering cost is $_______ (Enter your response rounded to two decimal places.)
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 $_____(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 490 bag lot size to the EOQ. (Enter your response rounded to two decimal places.)
Explanation / Answer
Purchase cost, p= $12.00
Ordering cost, O= $56/order
Annual holding cost, H = 26 percent of cost ==0.26*12= $ 3.12
Demand, d = 96 bags/week
Annual demand, D= 96*52 = 4992 bags per year
Standard deviation of weekly demand, d = 16 bags
Lead time = 4 week(s) (20 working days)
Desired cycle-service level=99 percent
Current on-hand inventory is 350 bags, with no open orders or backorders.
A. What is the EOQ?
sams optimal order quantity is ___424 _ bags (Enter your response rounded to the nearest whole number.)
The average time between orders is __4.40__ weeks. your response rounded to one decimal place.)
OPTIMAL QUANTITY, E.O.Q = SQRT(2 × annual demand × Cost Per Order / Holding Cost Per Order)
= SQRT(2 * 4992 * 56/3.12)
= 423.32
Time between orders, in weeks = Q/D =423.32/4992 =0.0848 YEARS=4.40 WEEKS
B. What should R be?
The reorder point is _459___ bags (Enter your response rounded to the nearest whole number.)
Reorder point (when demand varies, lead time is constant)
When demand varies, need to add safety stock. Amount of safety stock is dependent on the service level provided.
ROP = lead time demand+ safety stock
=d * LT + z * standards deviation of demand, d * LT
Z = 2.33 for 99% cycle service level (from normal distribution table)
ROP = d * LT + z * standards deviation of demand, d * LT
=96*4 + 2.33 * 16* 4 =458.56
C. An inventory withdrawal of 10 bags was just made. Is it time to reorder?
It is/ time to reorder
Initial inventory position = on hand inventory + scheduled receipts – backorders
=350+0-0
Withdrawal= 10 units
Remaining = 350 – 10 = 340.
Because inventory position 340 is below reorder point 459, it is time to place an order.
D. The store currently uses a lot size of 490 bags (i.e., Q=490). What is the annual holding cost of this policy? What is the annual ordering cost?
The annual holding cost is $_764.40_____ (Enter your response rounded to two decimal places.)
The annual ordering cost is $___570.51____ (Enter your response rounded to two decimal places.)
Annual holding cost
= (q/2) *H
= ( 490/2) * 3.12
=$764.40
Annual ordering cost
=number of orders * ordering cost per order
= (Annual demand / order quantity) * ordering cost per order
=(4992/490) * 56
=570.51
Total cost= Annual holding cost + Annual ordering cost
=$764.40 +570.51= $ 1334.91
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 $_661.44____(Enter your response rounded to two decimal places.)
Therefore, Sam's Cat Hotel saves $_14.15______ by shifting from the 490 bag lot size to the EOQ. (Enter your response rounded to two decimal places.)
EOQ
Annual holding cost
= (q/2) *H
= ( 424/2) * 3.12
=$661.44
Annual ordering cost
=number of orders * ordering cost per order
= (Annual demand / order quantity) * ordering cost per order
=(4992/424) * 56 =659.32
Total cost= Annual holding cost + Annual ordering cost
=$ 1320.76
The total cost is low when shifted from 490 bags per order to EOQ
SAVINGS= 1334.91-1320.76 = $14.15
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