At Dot Com, a large retailer of popular books, demand is constant at 17,000 book
ID: 355366 • Letter: A
Question
At Dot Com, a large retailer of popular books, demand is constant at 17,000 books per year. The cost of placing an order to replenish stock is $35, and the annual cost of holding is $6.00 per book. Stock is received 2 working days after an order has been placed. No backordering is allowed. Assume 250 working days a year a. Dot Com's optimal order quantity is 445 books. (Enter your response rounded to the nearest whole number) b. The optimal number of orders per year is 38 orders. (Enter your response rounded to the nearest whole number.) c. The optimal interval (in working days) between orders is 6.6 days. (Enter your response rounded to one decimal place.) d. The demand during lead time is 136 books. (Enter your response rounded to the nearest whole number) e. The reorder point is 136 books. (Enter your response rounded to the nearest whole number) f. The inventory position immediately after an order has been placed is books. (Enter your response rounded to the nearest whole number)Explanation / Answer
Annual demand (D) = 17000 books
Ordering cost (S) = $35
Holding cost (H) = $6
Lead time (L) = 2 days
Number of days per year = 250 days
Average daily demand (d) = D/250 days = 17000/250 = 68 books
a) Optimal order quantity (Q) = sqrt of (2DS / H)
= sqrt of [(2 x 17000 x 35)/6]
= 445 books
b) Number of orders per year = D/Q = 17000/445 = 38 orders
C) Interval between orders = (Q/D) Number of days per year
= (445/17000)250
= 6.5 days
d) Demand during lead time = Lxd = 2 days x 68 books = 136 books
e) Reorder point = d x L = 68 x 2 = 136 books
f) Inventory position immediately after an order has been placed = Reorder point + Q = 136 books + 445 books = 581 books
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