A sporting goods company has a distribution center that maintains inventory of f
ID: 355171 • Letter: A
Question
A sporting goods company has a distribution center that maintains inventory of fishing rods. The fishing rods have the following demand, lead time, and cost characteristics: Average demand = 230 units per day, with a standard deviation of 22 units Average lead time = 22 days with a standard deviation of 1 day 250 days per year Unit cost = $30 Desired service level = 97.5% Ordering cost = $57 Inventory carrying cost = 20%
+) Calculate annual ordering cost
+)Calculate average cycle stock.
+)Calculate average inventory.
Explanation / Answer
Given are following data :
Average Lead time = L = 22 days
Standard deviation of lead time = SdL = 1 day
Average demand per day = d = 230
Standard deviation of daily demand = Sdd = 22
Therefore ,
Standard deviation of demand during lead time
= Square root ( L x Sdd^2 + d^2 x Sdl^2)
= Square root ( 22 x 22^2 + 230^2x1^2)
= Square root ( 10648 + 52900)
= Square root ( 63548 )
= 252.08
Desired service level = 97.5%
Therefore, corresponding Z value = NORMSINV ( 0.975 ) = 1.96
Therefore, Safety stock = Z value x Standard deviation of demand during lead time = 1.96 x 252.08 = 494.07 ( 494 rounded t nearest whole number )
Also given are following data :
Annual demand = D = Daily demand x 250 days per year = 230 x 250 = 57500
Ordering cost = Co = $57
Annual unit inventory holding cost = Ch = 20% of unit cost of $30 = $6
Therefore , Economic Order Quantity ( EOQ )
= Square root ( 2 x Co x D / Ch )
= Square root ( 2 x 57 x 57500/ 6 )
= 1045.22 ( 1045 rounded to nearest whole number )
= Ordering cost x Number of orders
= Ordering cost x Annual demand / EOQ
= Co x D/EOQ
= 57 X 57500/1045
2. Average cycle stock = EOQ / 2 = 1045 /2 = 522.5
3. Average inventory = Average cycle stock + Safety stock = 522.5 + 494 = 1016.50
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