Abstract
We present two major revisions/corrections regarding a recent paper by T.C.E. Cheng [ Computers ind. Engng 18, 529–534 (1990)]. Firstly, we note that a critical assumption of equal replenishment cycle length for all products is stated, but not incorporated into the mathematical formulation in Cheng. In this paper, we re-formulate the problem with equal replenishment cycle length incorporated and derive the corresponding Kuhn-Tucker optimality conditions. Next, under linear demand assumption, we show that the closed-form solutions provided by Cheng may result in non-optimal solutions. The reason is that Cheng failed to derive conditions under which closed-form solutions may be optimal. In this paper, by employing trigonometric methods {see e.g. Chap. 2 of Griffiths [ Introduction of the Theory of Equations. Wiley, New York (1945).] or Appendix of Porteus [ Mgmt Sci. 31, 998–1010 (1985)]}, we derive an optimal closed-form solution that is unqiue and obtain conditions under which the optimal closed-form solution is valid.
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