Question

2. Joe Henry’s machine shop uses 10,000 brackets during the course of a year. These brackets are purchased from a supplier 90 miles away. The following information is known about the brackets: Annual demand 10,000 Holding cost per bracket per year $1.75 Order cost per order $22.00 Lead time 4 days Working days per year 250 a. Given the above information, what would be the economic order quantity (EOQ)? b. Given the EOQ, what would be the average inventory? What would be the annual inventory holding cost? c. Given the EOQ, how many orders would be made each year? What would be the annual order cost? d. Given the EOQ, what is the total annual cost of managing the inventory? e. What is the time between orders? f. What is the reorder point (ROP)?

Answer 1

(a) Annual Demand = D = 10000/year

Ordering Cost = C_o = $22

Holding Cost = C_c = $1.75/year

Economic Order Quantity Q* = √(2DC_o/C_c) = √(2*10000*22/1.75) = 501.43

(b) Average Inventory = Q*/2 = 501.43/2 = 250.72

Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*C_c = (501.43/2)*1.75 = $438.75

(c) Number of Annual orders = D/Q* = 10000/501.43 = 19.94

Annual Order cost = Number of orders * cost/order = (D/Q*) C_o = (10000/501.43)*22 = $438.75

(d) Total Annual Cost = Annual Inventory Holding Cost + Annual Order Cost = 438.75 + 438.75 = $877.5

(e) Time between orders = Cycle Time = Q*/D = 501.43/10000 = 0.050143 years = 0.050143*250 = 12.54 days

(f) Reorder Point = dL, where d = demand rate per period and L = lead time

Hence, Reorder point = (10000/250)*4 = 160