Algebraic modelling of a two level supply chain with defective items

¹ Department of Information Systems, King Faisal University, P.O. Box 78, Al-Hufof 31982, Saudi Arabia.
² College of Business Administration, Abu Dhabi University, P.O. Box 59911, Abu Dhabi, United Arab Emirates.
³ School of Engineering and Sciences, Tecnológico de Monterrey, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, Nuevo León, México

^* Corresponding author: e-mail: lecarden@itesm.mx

Received: 10 January 2017
Accepted: 7 September 2017

Abstract

M. Khan and M.Y. Jaber, Optimal inventory cycle in a two-stage supply chain incorporating imperfect items from suppliers. Int. J. Oper. Res. 10 (2011) 442–457, have addressed a two level supply chain of defective items. They compared three coordination mechanisms, i.e. cycle time; K–multiplier cycle time; and 2^K–multiplier cycle time. This paper proposes a simpler algebraic solution for the K–multiplier cycle time mechanism without the use of differential calculus. The two level supply chain with defective items is illustrated with a numerical example. A sensitivity analysis is also provided.