2. A sports apparel store is ordering 400 pairs of its best selling shoes every time it orders the shoes. The daily demand is 50 pairs, with a daily standard deviation of 5 pairs. It takes 4 days to receive a new order from its supplier. The order cost is $25, and the inventory holding cost is 25% of the cost of the shoes, which is $100 per pair. The store is open 350 days a year. a. How much money can you save the store by suggesting a new order quantity? b. Determine the rule for the inventory clerk in charge of this pair of shoes using Q system? Assume the store does not like to turn back customers, and therefore, they would like a 99% probability of not running out of stock.)

(a) Annual Demand = 50*350 = 17500

Actual Order Quantity = Q = 400 pairs

Order Cost = Co = $25

Holding Cost = Cc = 25% of 100 = $25

Annual Inventory Holding cost = average inventory * unit carrying cost = (Q/2)*Cc = (400/2)*25 = $5000

Annual Order cost = Number of orders * cost/order = (D/Q) Co = (17500/400)*25 = $1093.75

Total Cost = Annual Inventory Holding Cost + Annual Order Cost = 5000 + 1093.75 = $6093.75

Economic Order Quantity = Q* = √(2DCo/Cc) = √(2*17500*25/25) = 187.08

Annual Inventory Holding cost = average inventory * unit carrying cost = (Q*/2)*Cc = (187.08/2)*25 = $2338.5

Annual Order cost = Number of orders * cost/order = (D/Q*) Co = (17500/187.08)*25 = $2338.5

Total Cost = Annual Inventory Holding Cost + Annual Order Cost = 2338.5 + 2338.5 = $4677

Money saved with Economic Order Quantity = 6093.75 - 4677 = $1416.75

(b)

Safety Stock = zσd√L

Where z = number of standard deviations based on service level 99% = 2.33 from z table

σd = standard deviation of daily demand = 5

L = Lead Time = 4 days

Safety Stock = 2.33*5*√4 = 23.3

Reorder point = dL + zσd√L

where d = average daily demand = 50

Reorder Point = 50*4 + 2.33*5*√4 = 223.3

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