Consider an (s, Q) system of control for a single item and with normally distributed forecast errors.

a. Find an expression that k must satisfy given a Q value if we wish to have an expected number of stockout occasions per year equal to N.

b. Derive the two simultaneous equations that Q and k must satisfy if we wish to minimize the total expected costs of replenishment and carrying inventory subject to the expected number of stockout occasions per year being N.

c. For the following example, develop Q, k, and the associated total relevant costs per year for two strategies:

i. Q = EOQ and corresponding k ii. Simultaneous best (Q, k) pair Item characteristics:

A = $5 v = $2/unit r = 0.16$/$/year D = 1,000 units/year

σL = 80 units N = 0.5/year LOP52