In an (s, Q) system, it can be shown that the inventory position has a uniform distribution with probability 1/Q at each of the integers s + 1, s + 2, ... , s + Q − 1, s + Q.

a. Using this result, show, for Poisson demand and the B2 shortage cost measure, that ETRC(s) = vr s x0=0

(s − x0)pp0 (x0|ˆxL) + B2vD

Q j=1 1

Q

∞

x0=s+j pp0 (x0|ˆxL)

b. Show that indifference between s and s + 1 exists when Q

j=1 pp0 (s + j|ˆxL)

pp0≤(s|ˆxL) = Qr DB2

(Note: pp0 (x0|ˆxL) is the p.m.f. of a Poisson variable with mean xˆL.)