The economic production quantity with rework process in supply chain management

Abstract: 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 to find the economic production quantity with rework process at a manufacturing system and assumes that is convex. So, the solution satisfying the first-order-derivative condition for will be the optimal solution. However, this paper indicates that does not necessarily exist although 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 satisfying the-first-derivative condition of . [(B)] This paper tries to present a concrete solution procedure to find the optimal solution of . [Copyright &y& Elsevier]