A note on optimal ordering policies when the supplier provides a progressive interest scheme

Goyal et al. [Goyal, S.K., Teng, J.T., Chang, C.T., 2007. Optimal ordering policies when the supplier provides a progressive interest scheme. European Journal of Operational Research 179, 404–413] explore optimal ordering policies when the supplier provides a progressive interest scheme. The main purpose of this paper is fourfold: (1) This paper simplifies the total relevant cost per year Z(T) of Goyal et al. (2007) such that we can locate the optimal solutions of Z(T) by an easier way. (2) Goyal et al. (2007) use an algebraic approach to search for the optimal solution of Z(T). Their solution procedures ignore the explorations of the functional behavior of Z(T) such that their proofs fill shortcomings. This paper overcomes those shortcomings and presents a correct solution procedure for Goyal et al. (2007). (3) This paper demonstrates that the solution procedure in this paper can locate all optimal solutions of Z(T), however, that of Goyal et al. (2007) can only locate partially optimal solutions of Z(T). (4) Numerical examples reveal that Theorems 1(6) and 2(5) in Goyal et al. (2007) are not necessarily true, in general.