Question

a. How much safety stock provides a 95% service level to Thomas? b. What should the reorder point be? Question (3 The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D 600 units, S $20/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost? Quantity Price 1 to 49 50 to 249 250 and up $5.00 per unit $4.50 per unit $4.10 per unit Question

Answer 1

Here, Demand (D) = 600 units

Ordering cost (S) = $20

Holding cost (H) = 30%

Quantity	Price	Holding cost (30% of price)	EOQ = √ ((2*D*S) / H)		Order quantity
1 - 49	5.00	1.50	126.49	EOQ > upper limit of quantity = discarded	-
50 - 249	4.50	1.35	133.33	EOQ is within range of Quantity = EOQ	133.33
250 & up	4.10	1.23	139.69	EOQ < lower limit of Quantity = lower limit of Q	250

Q	Price	Order quantity	Ordering cost (Demand / order quantity) * Ordering cost	Holding cost (order quantity / 2) *Holding cost	Item cost (Demand * price)	Total cost (Ordering Cost + Holding Cost + Item Cost)
1 – 49	5.00	-	-	-	-	-
50 - 249	4.50	133.33	90	90	2700	2880.00
250 & up	4.10	250	48	153.75	2460	2661.75

In order to minimize the total annual cost, the firm should order 250 units at price $4.10 as the annual total cost of this option is $2,661.75 which is minimum of all.