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 2^{nd} 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