Given a product that costs $70.08 per unit and has an average lead time of 12 da
ID: 354219 • Letter: G
Question
Given a product that costs $70.08 per unit and has an average lead time of 12 days, standard deviation of lead time of 6 days, average demand of 144.4 units/day, standard deviation of demand of 11.6 units/day, stockout cost of $23.50 per unit, ordering cost of $270/order, inventory holding cost of 20% of item cost and needs to be in-stock 90% during lead time, calculate the following (you can leave all of these as decimals):
Assume the company is using a Continuous (EOQ) model to manage this inventory for parts a-d.
What is the economic order quantity? (2 points)
What is the expected number of units out of stock during an order cycle? (2 points)
What is the average inventory level? (2 points)
What is the annual service level? (2 points)
Assume the company is using a Periodic model to manage this inventory for parts e-f
What is the reorder period, in days? Answer must be shown in days. (2 points)
Assume lead time is constant at 12 days. What is s', the standard deviation of demand during lead time plus the reorder period? (2 points)
Explanation / Answer
Cost of Product, C = $70.08 per unit
Lead time , LT = 12 days
Standard deviation of leadtime sLT = 6 days
Average daily demand, D = 144.4 units per day
Standard Deviation of Demand, sd = 11.6 units/day
Stock out cost , k= $23.50 per unit
Ordering cost , S = $270 per order
Inventory holding cost , I = 20% of item cost
In stock Probability during lead time, P = 90%
1. What is the economic order quantity?
EOQ, Q = Sqrt(2DS/IC) = sqrt(2*144.4*270/(0.2*70.08)) = 74.6 units
2. What is the expected number of units out of stock during an order cycle? (2 points)
Expected Number of Units out of stock during an order = z*sd'
sd' = standard deviation of Demand during Lead time
sd' = Sqrt(LT*sd2 + D2 sLT2 ) = 867.3 units
value of z at P = 90% = 1.29
Expected Number of Units out of stock during an order = z*sd' = 1118.9 units
What is the average inventory level? (2 points)
Average Inventory AIL = Q/2 + z*sd' = 1156.2 units
What is the annual service level? (2 points)
SL = 1- (sd' *E(z)/Q )
E(z) unit normal loss integeral
E(z= 1.29 ) = 0.0465
SL = 1- (sd' *E(z)/Q ) = 46%
What is the reorder period, in days?
ROP = D*LT+ z*sd' = 2851.6 units
ROP in days = 2851.6 / D = 20 days
Standard deviation of leadtime sLT = 0
LT = 12
sd' = Sqrt(LT*sd2 + D2 sLT2 ) = sd*Sqrt(LT) = 11.6* Sqrt(12) = 40.2 units
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.