USA: +1 725-224-8795 
Sign in
Crew Soccer Shoes Company is reconsidering its current inventory control system and distribution strategy for soccer shoes. The information regarding the shoes is as follows:
Annual Demand = 1000 pairs/year
Lead time = 1 weeks
Order cost = $35/order
Holding cost = $2.00/pair/year
Service Level = 95%
Standard deviation of annual demand = 1000
Number of weeks/year = 50
If Crew currently has one warehouse and serves both the East and West Coast demand (which are equal and they assume normally distributed and independent), what will happen to demand, total inventory and safety stock if they open a second warehouse (which serves half the country)? Answer in paragraph form, then with math calculations.
Assume they use a fixed quantity Q, R system and each warehouse will serve one Coast.
Expert Answer
1 unit = a pair of shoes
Demand = D = 1000 units per annum
Lead Time LT = 1 week
D LT = Lead Time Demand = ?
Ordering Cost = O = $35
Inventory Holding cost or carrying cost = C = $2 per unit
Service level = confidence level = 95% = 1-alpha
alpha = 1-95% = 5% = 0.05
K for 95% from the standards normal table = 1.64
Standard deviation Chi = 1000
sqrt = square root
Economic Order Quantity (EOQ) = Q * = sqrt(2DO/C)
= sqrt(2*1000*35/2) = 177+10
Weekly Demand = D/number of weeks = 1000/50 = 20
Lead Time demand = D LT = Lead Time * weekly Demand = 1 * 20 = 20
Safety Stock = SS = K * Chi = 1.64 * 1000 = 1640
Reorder Level = ROL = D LT + SS = 20 + 1640 = 1660
When a 2nd warehouse is opened, the demand is shared by the 2 warehouses. D becomes D/2 = 1000/2 = 500
New D = 500
Q = sqrt(2*500*35/2) = 132
Weekly demand = 500/50 = 10
D LT = 1*10 = 10
SS = 1.64 * 1000 = 1640
ROL = 10 + 1640 = 1650
But when we assume that the standard deviation is also shared by both the warehouses, then
SS = 1.64 * 500 = 720+100
ROL = 10 + 720+100 = 730+100
