The XYZ Industrial Supplier Co. is a wholesaler/distributor located in Alberta,
ID: 361382 • Letter: T
Question
The XYZ Industrial Supplier Co. is a wholesaler/distributor located in Alberta, Canada, that supplies industrial clients with fasteners (nut, bolts, etc.), work gloves, and seemingly everything in between. Consider a specific high- quality work glove that has a special grip material on the palm and fingers, which makes it appropriate for use by moving companies, glass companies, and many other industries. XYZ sells these gloves from their inventory to their customers (in full cases only, where a case hold 12 pairs of gloves). Inventory of the gloves at the XYZ warehouse is replenished through orders with the manufacturer of the gloves, which is located in Syracuse, NY.
XYZ collected the following specific inventory-related data :
Weekly demand (in cases): average 17/week; standard deviation 7/week
Annual demand (in cases; assuming that demand occurs 52 weeks/year): 884
Purchase price (XYZ pays manufacturer) per case: $72 Canadian
XYZ cost to place order with manufacturer: $45 per order (includes administrative costs to issue purchase order, invoice payment, etc)
XYZ annual cost to hold inventory: 24% of value
Lead-time for replenishment from manufacturer: two weeks
Your Question: XYZ would like to implement an inventory control system whereby they check inventory of gloves every “ x” number of weeks and place an order with the manufacturer. Which of the following would be the most suitable number of weeks for the time between orders (rounded to the nearest week), so the total of annual holding and ordering costs is minimized?
every two weeks
every five weeks
every four weeks
every three weeks
every week
a.every two weeks
b.every five weeks
c.every four weeks
d.every three weeks
e.every week
Explanation / Answer
Annual demand (D) = 884 cases
Ordering cost (S) = $45
Holding cost (H) = 24% of price = 24% of $72 = $17.28
Number of weeks per year = 52 weeks
Economic order quantity (Q) = sqrt of (2DS / H)
= sqrt of [(2 x 884 x 45) / 17.28]
= 68 cases
Number of orders per year = D/Q = 884/68 = 13
Time between orders = Number of weeks per year / Number of orders per year
= 52 / 13
= 4 weeks
So the time between orders is 4 weeks. Answer is option c
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