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One of the most important aspects of multi-echelon inventory management deals with spare part; because, in the real world, it is more economic to repair equipment than change them. Also, it is possible, when more spare parts bought from an external supplier; seller gives quantity discount for all units. So, this paper considers a multi-echelon spare-part inventory system with backorders and quantity discount of external suppliers. Furthermore, a network approach is applied for modeling and solving these problems. Numerical example shows the efficiency of this algorithm.

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