Question

A company purchases a part from a special vendor. The average usage of the part is 900 units per year (assume 1 year = 50 weeks), with a standard deviation of 4 units per week. It costs the company $242 to place an order and $16 per unit per year to stock the item. If the lead-time for delivery is 4 weeks, find the economic order quantity and the reorder point for a service level of 95% no stock outs.

Answer 1

Following are the relevant details :

Annual demand = D = 900

Ordering cost = C = $242

Holding cost = H = $16

Economic order quantity = Square root ( 2 x D X C/H) = Square root ( 2 x 900 x 242 /16 ) = 165

Z value for service level 95% = 1.6448

Safety stock = z value x standard deviation x Square root ( Lead time ) = 1.6448 x 4 x square root ( 4 ) = 1.6448 x 4 x 2 =13.158

Average weekly demand = 900/50 = 18

Reorder point = Average weekly demand x Lead time ( weeks ) + safety stock = 18 x 4 + 13.158 = 72 + 13.158 = 85.158 ( 85 rounded to nearest whole number )

Answer :       Economic order quantity = 165 ,   Reorder point = 85