Question

A firm desires to control inventory levels so as to minimize the sum of holding and order costs. It costs the firm $20 to place an order. The firm estimates its inventory carrying costs at $2/unit/year. Weekly demand is 100 units and there are 50 weeks in the work year. The item costs $10 per unit. Leadtime for the product is 5 weeks. 32. What quantity of items should the firm order each time so as to minimize total inventory costs? A) 32 B) 45 C) 145 D) 224 E) 316 33. If 200 are ordered each time, then what will be the total annual holding cost. A) 50B) 100C) 200D) 250E) 500 34. If 1000 are ordered each time, then what will be the total annual order cost. A) 50B ) 100 C) 200D) 250E) 500 35. In order to not run out of stock before the receipt of a new order, at what inventory level should the firm place an order? That is, what is the reorder point equal to? A) 40 B) 100 C) 200 D) 400 E ) 500

Answer 1

Weekly demand (d) = 100

Annual Demand (D) = 100*50 = 5000 units

Ordering Cost (S) = $20

Holding Cost (H) = $2

Lead time (L) = 5 weeks

Item cost (p) = $10

Answer 32: E. 316

$\small Q = \sqrt{\frac{2*S*D}{H}} =\sqrt{\frac{2*20*5000}{2}} = 316.22 \approx 316$

Answer 33: C.200

Q = 200

Annual Holding Cost = (Q/2)*H = (200/2)*2 = $200

Answer 34: B.100

Q = 1000

Annual Ordering Cost = (D/Q)*S = (5000/1000)*20 = $100

Answer 35: E.500

Reorder Point = Average demand during lead time = d*L = 100*5 = 500