Erratum to: An optimal inventory management problem with reputation-dependent demand

Abstract

1. In this paper, we derived necessary optimality conditions for the stated problem. Therefore, the phrase “optimal solution” used in the paper should have the meaning of local optimum. 2. The argument proven in Lemma 2 is not sufficient for global optimality of a reputationdependent base-stock policy. Generally, the globally optimal policy may depend on the two state variables: x—the inventory level and r—the value of reputation, rather than only on r as shown in the paper. Consequently, the statement that the optimal solution is a reputation-dependent base-stock policy is incorrect. In case the optimal policy depends on the two state variables, the necessary optimality conditions (18) and (19) remain without change, except that y(r) and ψ2(r) are replaced by y(r, x) and ψ2(r, x), as follows: (p − c) 1− βEπ [ F ′ (y(r, x)− rξ) = Eπ [ C ′ (F(y(r, x)− rξ)) F ′(y(r, x)− rξ) +β(1− γ )Eπ [ G ′ (F(y(r, x)− rξ)) F ′(y(r, x)− rξ)ψ2(γ r + (1− γ )G (F(y(r)− rξ)) , F(y(r, x)− rξ)) (18a)