Sam\'s Cat Hotel operates 52 weeks per year, 5 days per week, and uses a continu
ID: 369732 • 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 $11.00 per bag. The following information is available about these bags.
Demand = 100 bags/week
Order cost = $58/order
Annual holding cost = 28 percent of cost
Desired cycle-service level=96 percent
Lead time = 4 week(s) (20 working days)
Standard deviation of weekly demand = 10 bags
Current on-hand inventory is 310 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
Consider the following Notation:
A) Sam’s Optimal order quantity (EOQ):
EOQ = sqrt(2DS/H)
= Sqrt(2*100*$58)/$3.08 = 61.37
Optimal Order quantity, EOQ = 61 units (round off)
To calculate average time between orders:
Time between orders = (number of working weeks per year) / (total number of orders per year)
Before we calculate this, we should calculate the total number of orders per year:Total number of orders = D/Q, where, D = Annual Demand = (100*52) = 5200 bags per year; Q = 61 bags (as calculated in part a)
Total number of orders = 5200/61 = 85.24 orders
With this we can calculate average time between orders = 52/85.24 = 0.61 weeks ~ 4.27 days
B) Reorder point R:
R = dL + z*SD*sqrt(L)
= [(100/52)*4] + [1.751*10*sqrt(4)]
R = 42.71 = 43 units (round off)
C) An inventory withdrawal of 10 bags is not the time to reorder as the current onhand inventory is 310.
D) Q = 490
Annual holding cost = (Q/2)H = (490/2)*3.08 = 754.6 ~ $755
Annual ordering cost = (D/Q)S = (100/490)*58 = $11.84 ~ $12
We can say the current lot is large because ordering cost is too less when compare with holding cost.
E) Q = EOQ = 490 units
Annual holding cost = (Q/2)H = (490/2)*3.08 = 754.6 ~ $755
Annual ordering cost = (D/Q)S = (100/490)*58 = $11.84 ~ $12
Total cost = $755 + $12 = $ 767
For the current EOQ as per the details in the problem,
Annual holding cost = (Q/2)H = (61/2)*3.08 = 93.94 ~ $94
Annual ordering cost = (D/Q)S = (100/61)*58 = $95.08 ~ $95
Total Cost = $ 94 + $ 95 = $ 189
Savings = $767 - $189 = $578
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