The economic production quantity with rework process in supply chain management

Cardenas-Barron [L.E. Cardenas-Barron, Economic production quantity with rework process at a single-stage manufacturing system with planned backorders, Computers and Industrial Engineering 57 (2009) 1105–1113] minimizes the annual total relevant cost TC(Q , B) to find the economic production quantitywith rework process at amanufacturing system and assumes that TC(Q , B) is convex. So, the solution (Q̄ , B̄) satisfying the firstorder-derivative condition for TC(Q , B) will be the optimal solution. However, this paper indicates that (Q̄ , B̄) does not necessarily exist although TC(Q , B) is convex. Consequently, the main purpose of this paper is two-fold: (A) This paper tries to develop the sufficient and necessary condition for the existence of the solution (Q̄ , B̄) satisfying the-first-derivative condition of TC(Q , B). (B) This paper tries to present a concrete solution procedure to find the optimal solution of TC(Q , B). © 2011 Elsevier Ltd. All rights reserved.