Problem 2: Inventory Management A distributor uses a continuous review system to
ID: 422227 • Letter: P
Question
Problem 2: Inventory Management A distributor uses a continuous review system to manage its inventory. Parts are purchased with the entire order arriving at the same time (instantaneous replenishment). The information represents one SKU, stock keeping unit, of critical importance. Unit Cost of Material Annual Demand $250 100,000 units Standard Deviation of Daily Demand Business Days Per Year 250 7 days 2 da 500 per order Average Material Lead Time Standard Deviation of Lead Time Annual Holding Cost 2A. Determine the reorder point, assuming that there is NO safety stock. (3 points) Setup Cost (As% of Purchase Cost) ear kini 2B. Determine the optimal order quantity. (4 points) elc of th ddre 2C. Determine the safety stock for a service level of 97.5%. The safety stock must protect against uncertainties in both lead time and daily demand. demand is normally distributed and the ch of (4 points) effec 2D. The suppler offered a 15% discount if the company orders a minimum of 2000 units each time. Determine if it is an economically attractive offer. (3 points) 7 of 10Explanation / Answer
2A-
Re order point = Avg demand x avg. lead time + Safety stock
As there is no safety stock, the ROP will be equal to
ROP = Avg demand x avg. lead time = 100000/250 x 7 =2800 units
2B
EOQ = [ 2x annual demand x ordering cost / annual holding cost of one unit ]1/2
= [ 2x 100000 x500/100]1/2 = 1000
2C
Safety stock = z x [ ( s.d of lead time)2 x(dbar)2 + ( s.d of demand)2 x Lbar]1/2
= 1.96[ 4 x (400)2+ (20)2 x7]1/2 = 1.96 x 801 = 1571
2D
No. of orders in case I = 100000/1000 =100
Ordering cost = 100x500 = 50000
Holding cost = 1000/2 x 100 =50000
Total cost = ordering cost + holding cost = 100000
In case II ( 2000 units)
No. of orders = 100000/2000 = 50
Ordering cost = 500x50 =25000
Holding cost = 2000/2 x100 = 100000
Total cost = 125000
Benefits derived from discount = 15/100 x250 x100000 = 3750000
The proposition is lucrative as more cost is saved agianst the expenses.
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