Answer:
(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
