Document Type : Original Article


1 Ph.D. Student, Kish International Campus, Tehran University.

2 Professor, Tehran University.

3 Professor, University of Tehran.


Inventory control is one of the important issues in supply chain management. The present study deals with designing and comparing a multi-level multi-product inventory simulation model in Iran steel industries. The divergent supply chain network model is considered with several final products, several middle products and one primary product. The purpose is to minimize cost function by maintaining the minimum level of service offering for each facilitation that is measured by means of fill rate. It is tried in the proposed model to achieve a local optimal point by having a possible point and second-order localization of the target function and linear constraints around that point as well as the use of genetics algorithm. Since point estimations of the target function and fill rates are carried out with the help of Monte Carlo simulation, statistical hypothesis testing is employed to test the possibility and improve the responses. After validation is fulfilled, the model is implemented in a three-level network via the information of Mobarakeh Steel Company. Given that linear localization is a specific state of second-order localization, it can be expected with more confidence that the achieved point in this model is better than the linear localization state. 


1. Almeder, C., Preusser, M., & Hartl, R. F. (2009).Simulation and optimization of supply chains: Alternative or complementary approaches? OR Spectrum, 31, 95-119.
2. Altendorfer, K., Minner, S., (2011). Simultaneous optimization of capacity and planned lead time in a two-stage production system with different customerdue dates. Eur. J. Oper. Res. 213, 134–146.
 3. Amiri, M., Seif barghy, ·M., Olfat, L., Razavi Hajiagha, S.H. (2012). "Determination of a desirable inventory policy in a three echelon multilayer supply chain with normal demand. International Journal of Industrial Engineering and Production Research, 23(1), 65-72.
4. Axsate r,. S. (2006). Inventory control. 2nd edition, New York: Spriner.
5. Axsater, S. (1990). Simple Solution Procedure for a Class of Two-Echelon Inventory Problem. Operatians Research, 38(1), 64-69.
6. Axsater, s. (2002). "Approximate optimization of a two-level distribution inventory system. International Journal of Production Economics, 81-82, 545-553.
7. Benton, W.C., Park, Seungwook, 1996. A classification of literature on determining the lot size under quantity discounts. European Journal of Operational Research 92(2), 219–238.
8. Bollapragada,S., Morton, TE. (1993). The periodic review inventory problem with random yield: near-myopic properties, heuristics and testing. WP # 199311,Graduate School of Industrial Administration and The Robotics Institute, Carnegie Mellon University.
9. Cachon, G.P. (2001). Exact Evaluation of Batch-ordering Inventory Policies in Two-Echelon supply chains with Periodic Review. Operations Research: 49(1), 79-98.
10. Chu, Y., You, F., & Wassick, J. M. (2014). Hybrid method integrating agent-based modeling and heuristic tree search for scheduling of complex batch processes. Computers & Chemical Engineering, 60, 277-296.
11. Chu, Y., You, F., Wassick, J.M., & Agarwal, A. (2014). Integrated planning and scheduling under production uncertainties: Bi-level model formulation and hybrid solution method. computers & chemical Engineering, DOI: 10. 1016 /j. compchemeng. 2014.02.023. With general network structure via agent-based modeling. AIChE Journal, 59, 2884-2906.
12. Chu,Y., You, F., wassick, J.M., & Agarwal.A. (2014). Simulation – based optimization framework for multi – echelon inventory systems under uncertainty. Computer & chemical Engineering, 73, 1-16.
13. Clark, A. J., Scarf, H. (1960). Optimal policies for a multi-echelon inventory problem. Management science, 6(4), 475-490
14. 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. Presented in: Schwarz, L.B. (1981). Multilevel Production/Inventory Control systems: Theory and Practice, Elsevier science Ltd.
15. Ehrenberg, C., Zimmermann, J., (2012). Simulation-based optimization in make-toorder production: scheduling for a special-purpose glass manufacturer. In: Laroque, C., Himmelspach, J., Pasupathy, R., Rose, O., Uhrmacher, A. (Eds.), Proceedings of the 2012 Winter Simulation Conference, December 2012. IEEE, pp. 1–12.
16.  Fakhrzad, M., & Zare, H. (2009). Combination of genetic algorithm grange multipliers for lot-size determination in multi-stage productioning problems. Expert Systems with Applications, 36, 10180–10187.
17. Gao, J., Wang, w. D. (2008). Simulation-based optimization and its application in multi-echelon network stochastic inventory system. 7th International conference on system simulation and scientific computing, 10-12 October, china, Beijing, 1302-1307.
18.  Ghiami, Y., Williams, T., & Wu, Y. (2013). A two-echelon inventory model for a deteriorating item with stock-dependent demand, partial backlogging and capacity constraints. European Journal of Operational Research.
19.   Gören, H.G., Tunalı, S.,And Jans, R., (2008). A review of applications of genetic algorithms in lot sizing. Journal of Intelligent Manufacturing,Vol.21,no.4,pp. 575-590.
20. Graves, S. C. (1985). A Multi-Echelon Inventory Model for a Repairable Item with one-for-one Replenishment. Management science, 31(10), 1247-1256.
21. Gumus, A.T., Guneri, A.F. (2007). Multi-echelon inventory management in supply chains with uncertain demand and lead times: literature review from an operational research perspective. Proceedings - Institution of Mechanical Engineers Part B: Journal of Engineering Manufacture, 221(10): 1553-1570
22.  Hoque, M.A., Goyal, S.K., (2000). An optimal policy for a single vendor single buyer integrated production inventory system with capacity constraint of the transport equipment. Inter-national Journal of Production Economics 65, 305–315.
23. Ivanov, D., Dolgui, A., & sokolov, B. (2012). Applicability of optimal control theory to adaptive supply chain planning and scheduling. Annual Reviews in control, 36, 73-84.
24. Jung, J. Y., Blau, G., Pekny, J. F., Reklaitis, G., & Eversdyk, D. (2008). Integrated safety stock management for multi-stage supply chains under production capacity constraints. Computers & chemical Engineering, 32, 2570-2581.
25. Jung, J. Y., Blau, G., Pekny, J. F., Reklaitis, G., V. & Eversdyk, D. (2004). A Simulation based optimization approach to supply chain management under demand uncertainty. Computers & chemical Engineering, 28, 2087-2106.
26. Kochel, P., Nielander, U. (2005). Simulation-based optimisation of multi-echelon inventory systems. International Journal of Production Economics. 93-94 (1), 505-513.
27. Liao, S.-H., Hsieh, C.-L., & Lin, Y.-S. (2011). A multi-objective evolutionary optimization approach for an integrated location-inventory distribution network problem under vendor-managed inventory systems. Annals of Operations Rasearch, 186, 213–229.
28. Lu, L., (1995). Theory and methodology: A one vendor multibuyer integrated inventory model. European Journal ofOperational Research 81 (2), 312–323.
29.  Mele, F. D., Guillen, G., Espuna, A., & Puigjaner, L. (2006). A simulation-based optimization framework for parameter optimization of supply-chain networks. Industrial & Engineering chemistry Research, 45, 3133- 3178.
30. Melouk, S., Freeman, N., Miller, D., Dunning, M., (2013). Simulation optimizationbased decision support tool for steel manufacturing. Int. J. Prod. Econ. 141 (1), 269–276.
31. Moin, N.H., Salhi, S., Aziz, N.A.B. (2011). An efficient hybrid genetic algorithm for the multi–product multi–period inventory routing problem. International Journal of Production Economics 133, 334–343.
32. Nachiappan, S., & Jawahar, N. (2007). A genetic algorithm for optimal operating parameters of vmi system in a two-echelon supply chain. European Journal               ofOperationalResearch,182,1433–145.
        33. Nikolopoul, A., & Ierapetritou, M. G. (2012). Hybrid simulation based optimization approach for supply chain management. Computers & chemical Engineering, 47, 183-193.
34. Pasandideh, S. H. R., Niaki, S. T. A., & Nia, A. R. (2011). A genetic algorithm for vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Systems with Applications, 38, 2708 –2716.
35. Perea-Lopez, E., Ydstie,B.E., & Grossmann, I.E. (2003). A model predictive control strategy for supply chain optimization. Computers & chemical Engineering, 27, 1201- 1218.
36. Rajendran, C.,Daniel, S,.(2005). A simulation-based genetic algorithm for inventory optimization in a serial supply chain. International Transactions in Operational Research,Vol 12, Issue 1, pages 101–127.  
 37. Schwartz, j.D., Wang, W.L.& Rivera, D.E. (2006). Simulation- based optimization of process control policies for inventory management in supply chains. Automatica, 42, 1311- 1320.
38. Sherbrook, C.C. (1968). Metric: A Multi- Echelon Technique for Recoverable Item Control. Operations Research, 16(1), 122- 141.
39. Silva,C.A., Sousa, J.M.C. Runkler, T.A., & Dacosta, J. (2006). Distributed optimization of a logistic system.
 40. Sue-Ann, G., Ponnambalam, S., & Jawahar, N. (2012). Evolutionary algorithms for optimal operating parameters of vendor managed inventory systems in a two-echelon supply chain. Advances in Engineering Software, 52, 47 – 54.
41. Syarif, A., YoungSu, Y. and Gen, M. (2002) ‘Study on Multi-Stage Logistic Chain Network: A Spanning Tree-Based Genetic Algorithm Approach. Computers and Industrial Engineering, 43(1-2), 299-314.
42. Wang, W., Fung, R.Y.K., Chai, Y., (2003). Approach of just-in-time distribution requirements planning for supply chain management. Int. J. of Production Economics, 91, 101-107.
43. Wang, K., & Wang, Y. (2008). Applying genetic algorithms to optimize the cost of multiple sourcing supply chain systems: An industry case study. Studies in Computational Intelligence, 92, 355–372.
44. Yimer, A. D., & Demirli, K. (2010). A genetic approach to two-phase optimization of dynamic supply chain scheduling. Computers & Industrial Engineering, 58, 411–422.    
45. Yokoyama, M. (2002). Integrated optimization of inventory distribution systems by random local seach and a genetic algorithm. Computers & Industrial Engineering, 42, 172–188.