This problem conducts a partial sensitivity analysis ofthe DEL model: Let d denote the entire sequence of demands {d(t), 0 :5 t < T}, regarded as a nonnegative T-vector, and C*

(d) the optimal cost of the DEL model with demand sequence

d, assuming the cost paranleters are fixed. Argue that C*

(d) is a continuous, nondecreasing, concave function of

d. (Hint: Let 'IT denote any fixed sequence of order times, and C(dl'IT) the cost of using the order times 'IT to meet the demand sequence

d. Express C*

(d) in terms of the C(dl'IT). Now, derive certain relevant properties of the C(dl'IT), and use these to arrive at the desired conclusion.)

What does this tell us about C*(2d), assuming we know C*(d)? Compare this finding to the effect of doubling ,\ in the EOQ model.