On "The Censored Newsvendor and the Optimal Acquisition of Information"

We have read Ding et al. (2002), referred to hereafter as DPB, with great interest. DPB con ains two main results: Theorem A claims that the myopic inventory level is a lower bound on the optimal inventory level, and Theo rem B attempts to quantify the marginal expected value of information. However, there are mistakes in the proof of Theorem A. The result itself is correct; a proof is given in Lu et al. (2004). Furthermore, one of the erroneous expressions in DPB's proof leads to an error in the marginal expected value of information in Theorem B. We now provide more details. The equation numbers, unless specified otherwise, refer to the appendix of DPB, available at the Operations Research home page (http://or. pubs.informs.org). The main error in the proof of Theorem A is the follow ing. If a{x) and b{x) are two functions of the variable jc, then the derivative of a(x)b(x) with respect to x is d r / x, / m , / ,da{x) .db(x) ? [a(x)b(x)] = b(x) -?? + a(x) -^. DPB's mistake, in essence, is to omit the second term. More specifically, a key step in proving Theorem A is inequality (35):