A certain chain of sports stores is considering changing its current inventory control system to manage its inventory of bicycle and sports helmets. The information regarding the helmets is as follows:

Average demand: 100 units/week

Lead time = 5 weeks

Order cost = $65/order

Unit cost = $90

Carrying rate = 10%

Standard deviation of weekly demand = 30

Desired service level = 95% (z-value= 1.645)

Number of weeks per year = 52

Inventory position (IP) = 300 units

Using a fixed-period inventory system model, calculate the optimal time interval (T) and replenishment level (M) for a fixed-period inventory model with and without safety stock.

a) Comment briefly on your findings and how this system operates.

b) Is the fixed-period inventory system model is suitable for this store? Consider the benefits and challenges of three inventory models.