Inventory management problem A sporting goods company has a distribution center
ID: 393986 • Letter: I
Question
Inventory management problem
A sporting goods company has a distribution center which maintains inventory of fishing rods. The fishing rods have the following demand, lead time and cost characteristics:
Average demand = 100 units per day, with a standard deviation of 12 units
Average lead time = 12 days with a standard deviation of 2 days
250 days per year in the business year
unit cost = $25
desired service level = 95%
Ordering cost = $50
Inventory carrying cost = 20%
How many fishing rods should the distribution center carry to provide the desired service level?
What is the EOQ?
What is the total acquisition cost (please include the annual product cost in your calculations)?
Please show the math in details
Explanation / Answer
Demand (D) = 100
Price (P) = 25
Ordering cost (S) = 50
Inventory carrying % is 20%
Holding cost (H) = P*20% = 25*20% = 5
Annual demand (d) = D*Number of working days = 100*250 = 25000
SD of demand (SD) = 12
Lead time (LT) = 12
SD of Lead time (s) = 2
Service level is 95%. z value for 95% is 1.64 (Using z table or NORMSINV function in excel)
a) Re order point or quantity in hand = D*LT + z*sqrt(LT*SD^2 + D^2*s^2) = 100*12 + 1.64*sqrt(12*(12)^2 + (100)^2*(2)^2) = 1535 units
b) EOQ = sqrt(2*d*S/H) = sqrt(2*25000*50/5) = 707 units
c) Total cost = d/EOQ*S + EOQ/2*H + P*d = 25000/707*50 + 707/2*5 + 25000*25 = 628,536 $
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