Algebraic modelling of a two level supply chain with defective items

Seliaman, Mohamed E.; Khan, Mehmood; Cárdenas-Barrón, Leopoldo Eduardo

RAIRO - Operations Research - Recherche Opérationnelle, Tome 52 (2018) no. 2, pp. 415-427.

M. Khan and M.Y. Jaber, Optimal inventory cycle in a two-stage supply chain incorporating imperfect items from suppliers. $\mathrm{𝐼𝑛𝑡}.𝐽.\mathrm{𝑂𝑝𝑒𝑟}.\mathrm{𝑅𝑒𝑠}.$ $\mathbf{10}$ (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.

Classification : 90B05
Mots clés : Supply chain management, integer multipliers, without derivatives, algebraic method

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