Algebraic modelling of a two level supply chain with defective items.

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.