Document Type : Original Article


1 M.A., Shahid Beheshti University.

2 Assistant Professor, Shahid Beheshti University.


In this paper, an inventory control model for a two-tier system is presented that applies the policy (R, Q) at each level to the IHP of each non-repair spare part, which has assumptions that limit its application to real-life situations. Slow. This research has expanded and extended this model by assuming discrete orders and warehouse space constraints. In the new situation, modeling was performed and then to solve the model obtained, the heuristic Genetic Algorithms (GA) were used ( ICAs) were developed and implemented. Also, their performance is evaluated by comparing the performance of the two algorithms.


1. Al-Rifaia, M، H. , Rossetti, M. (2007), "An efficient heuristic optimization algorithm for a two-echelon (R, Q) inventory system ".Int. J. Production Economics, 109, 195–213.
2. Anderson, J., Marklund, J. (2000), "Decentralized inventory control in a two-level distribution system", European Journal of Operational Research, 127,483–506.
3. Atashpaz-Gargari, E., Lucas, C. (2007), "Imperialist Competitive Algorithm: An algorithm for optimization inspired by imperialistic competition", IEEE Congress on Evolutionary Computation, Singapore.
4. Caglar, D., Li, C.-L., Simchi-Levi, D. (2004), "Two-echelon spare parts inventory system subject to a service constraint", IIE Transactions, 36, 655–666.
5. Deuermeyer, B.L., Schwarz, L.B. (1981), "A model for the analysis of system service level in warehouse-retailer distribution systems: The identical retailer case", TIMS Studies in the Management Sciences, 16, 163–193.
6. Diaz, A., Fu, M.C. (1997), "Models for Multi-echelon repairable item inventory systems with limited repair capacity", European Journal of Operational Research, 97, 480–492.
7. Graves, S.C. (1985), "A multi-echelon inventory model for a repairable item with one-for-one replenishment", Management Science, 31, 1247–1256.
8. Hopp, W.J., Spearman, M.L. and Zhang, R.Q. (1997), "Easily implementable inventory control policies", Operations Research, 45, 327–340.
9. Hopp, W.J., Spearman, M.L. (2001), "Factory Physics", second ed. McGraw-Hill, New York.
10. Hopp, W.J., Zhang, R.Q. and Spearman, M.L. (1999), "An easily implementable hierarchical heuristic for a two-echelon spare parts distribution system" IIE Transactions, 31,977–988.
11. Sherbrooke, C.C. (1986), " METRIC: A multi-echelon technique for recoverable item control" Operations Research, 16, 122–141.
12. Svoronos, A., Zipkin, P. (1988), "Estimating the performance of multi-level inventory systems", Operations Research, 36 , 57–72.