42) Chuck No Risk (CNC) has collected the following information on one of its pr
ID: 380356 • Letter: 4
Question
42) Chuck No Risk (CNC) has collected the following information on one of its products: Demand = 4,500 units/year Standard deviation of weekly demand 12 units Ordering costs $40/order Holding costs $3/unit/year Cycle-service level = 90%, Lead-time = 2 weeks Number of weeks per year 52 weeks a. If CNC uses the continuous review system to control the inventory, how many should be ordered and when? b. CNC decided to change to the periodic review system to control the item's inventory. For the most recent review, an inventory clerk checked the inventory of this item and found 300 units. There were no scheduled receipts or backorders at the time. How many units should be ordered?Explanation / Answer
Answer to Q.a:
Given are following data :
Demand = D = 4500 unit/ year
Ordering cost = Co = $40/ order
Annual unit holding cost = Ch = $3 / unit/year
Thus , Optimum order quantity
= Square root ( 2 x Co X D / Ch)
= Square root ( 2 x 40 x 4500 / 3 )
= 346.41 ( 346 rounded to nearest whole number )
QUANTITY TO BE ORDERED = 346
Answer to Q.b
Cycle service level = 90% ( i.e. service probability = 0.90)
Corresponding Z value = NORMSINV ( 0.90) = 1.2815
Standard deviation of weekly demand = 12 units
Lead time = 2 weeks
Hence, Standard deviation of demand during lead time
= Standard deviation of weekly demand x Square root ( Lead time )
= 12 x Square root ( 2 )
= 12 x 1.414
= 16.968
Hence, safety stock
= Z value x Standard deviation of demand during lead time
= 1.2815 x 16.968
= 21.744
Average weekly demand = Annual demand / 52 weeks = 4500/ 52
Thus, Reorder point
= Average weekly demand x Lead time ( weeks ) + Safety stock
= 4500/52 x 2 + 21.744
= 173.076 + 21.744
= 194.82 ( 195 rounding to next higher whole number )
Given, Inventory on hand = 300
Since, Inventory on hand ( i.e. 300) < Reorder point ( 195), no items need to be ordred
QUANTITY TO BE ORDERED = 346
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