Ck. Chen et Kj. Min, A MULTIPRODUCT EOQ MODEL WITH PRICING CONSIDERATION - CHENG,T.C.E. MODEL REVISITED, Computers & industrial engineering, 26(4), 1994, pp. 787-794
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 f
or 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 correspon
ding Kuhn-Tucker optimally conditions. Next, under linear demand assum
ption, we show that the closed-form solutions provided by Cheng may re
sult in non-optimal solutions. The reason is that Cheng failed to deri
ve conditions under which closed-form solutions may be optimal. In thi
s paper, by employing trigonometric methods {see e.g. Chap. 2 of Griff
iths [Introduction of the Theory of Equations. Wiley, New York (1945).
] or Appendix of Porteus [Mgmt Sci. 31, 998-1010 (1985)]{, we derive a
n optimal closed-form solution that is unique and obtain conditions un
der which the optimal closed-form solution is valid.