Waterloo Warehouse Ltd. (WWL) acts as a distributor for a product manufactured by Norwich Company. WWL uses an (s, Q) type of control system. Demands on Waterloo can be assumed to be unit sized. Norwich has a particular way of delivering the quantity Q:

They deliver Q/2 at the end of the lead time of 1 month and the other Q/2 at the end of 2 months. Assume that this business has the following characteristics:

Q = 100 units s = 40 units

σ1 = 10 units (σ1 = the standard deviation of forecast errors over 1 month)

D = 360 units/year v = $1.00/unit r = 0.25 $/$/year

a. What is the numerical value of the SS? Explain your answer.

b. Suppose that a replenishment is triggered at t = 0, and no order is outstanding at this time. Describe in words what conditions must hold in order for there to be no stockout up to time t = 2 months.

c. Suppose that Norwich offered WWL the option to receive the whole quantity Q after a lead time of 1 month, but at a higher unit price. Outline the steps of an analysis to decide whether or not the option should be accepted.