A MULTIPRODUCT EOQ MODEL WITH PRICING CONSIDERATION - CHENG,T.C.E. MODEL REVISITED

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 optimally 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 unique and obtain conditions under which the optimal closed-form solution is valid.