An Integrated Approach to Robust Multi-echelon Inventory Policy Decision

  • Katja Klingebiel
  • Cong Li
Part of the Studies in Computational Intelligence book series (SCI, volume 416)


To cope with current turbulent market demands, robust multi-echelon inventory policies are needed for distribution networks in order to lower inventory costs as well as to maintain high responsiveness. This paper analyzes the inventory policies in the context of complex distribution networks and proposes a new integrated approach to robust multi-echelon inventory policy decision, which is composed of three interrelated components: an analytical inventory policy optimisation, a supply chain simulation module and a metaheuristic-based inventory policy optimiser. Based on the existing approximation algorithms designed primarily for two-echelon inventory policy optimisation, an analytical multi-echelon inventory model in combination with an efficient optimisation algorithm has been designed. Through systematic parameter adjustment, an initial generation of optimised multi-echelon inventory policies is calculated. To evaluate optimality and robustness of these multi-echelon inventory policies under market dynamics, they are automatically handed over to a simulation module, which is capable of modeling arbitrary complexity and uncertainties within and outside of a supply chain and simulating them under respective scenarios. Based on the simulation results, i.e. the robustness of the proposed strategies, a metaheuristic-based inventory policy optimiser regenerates improved (more robust) multi-echelon inventory policies, which are once again dynamically evaluated through simulation. This closed feedback loop forms a simulation optimisation process that enables the autonomous evolution of robust multi-echelon inventory policies. The proposed approach has further been validated by an industrial case study, in which favorable outcomes have been obtained.


Supply Chain Distribution Network Inventory Policy Inventory Cost Reorder Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Al-Harkan, I., Hariga, M.: A simulation optimization solution to the inventory continuous review problem with lot size dependent lead-time. Arabian Journal for Science and Engineering 32, 329–338 (2007)Google Scholar
  2. 2.
    Al-Rifai, M.H., Rossetti, M.D.: An efficient heuristic optimization algorithm for a two-echelon (r, q) inventory system. International Journal of Production Economics 109, 195–213 (2007)CrossRefGoogle Scholar
  3. 3.
    April, J., Glover, F., Kelly, J.P., Laguna, M.: Practical introduction to simulation optimization. In: Proceedings of the 2003 Winter Simulation Conference, pp. 71–78 (2003)Google Scholar
  4. 4.
    Axsäter, S.: Simple solution procedures for a class of two-echelon inventory problems. Operations Research 38, 64–69 (1990)zbMATHCrossRefGoogle Scholar
  5. 5.
    Axsäter, S.: Exact and approximate evaluation of batch-ordering policies for two-level inventory systems. Operations Research 41, 777–815 (1993)zbMATHCrossRefGoogle Scholar
  6. 6.
    Axsäter, S.: Evaluation of installation stock based (r, q)-policies for two-level inventory systems with poisson demand. Operations Research 46, 135–145 (1998)CrossRefGoogle Scholar
  7. 7.
    Axsäter, S.: Exact analysis of continuous review (r, q)-policies in two-echelon inventory systems with compound poisson demand. Operations Research 48, 686–696 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Axsäter, S.: Approximate optimization of a two-level distribution inventory system. International Journal of Production Economics 81-82, 545–553 (2003)CrossRefGoogle Scholar
  9. 9.
    Axsäter, S.: Supply chain operation: Serial and distribution inventory systems. In: Handbooks in OR & MS, vol. 11, pp. 525–559. Elsevier (2003)Google Scholar
  10. 10.
    Axsäter, S.: A simple decision rule for decentralized two-echelon inventory control. International Journal of Production Economics 93/94, 53–59 (2005)CrossRefGoogle Scholar
  11. 11.
    Axsäter, S.: Inventory control. International Series in Operations Research & Management Science, 2nd edn., vol. 90. Springer (2006)Google Scholar
  12. 12.
    Barton, R.R., Meckesheimer, M.: Metamodel-based simulation optimization. In: Handbooks in OR & MS, vol. 13, pp. 535–574. Elsevier (2006)Google Scholar
  13. 13.
    Caglar, D., Li, C.L., Simchi-Levi, D.: Two-echelon spare parts inventory system subject to a service constraint. Institute of Industrial Engineers 36, 655–666 (2004)Google Scholar
  14. 14.
    Chopra, S., Meindl, P.: Supply chain management: Strategy, planning, and operation, 4th edn. Pearson, Boston (2010)Google Scholar
  15. 15.
    Chopra, S., Sodhi, M.S.: Managing risk to avoid supply chain breakdown. Sloan Management Review 46(1), 53–61 (2004)Google Scholar
  16. 16.
    Cirullies, J., Klingebiel, K., Scarvarda, L.F.: Integration of ecological criteria into the dynamic assessment of order penetration points in logistics networks. In: Proceedings of 25th European Conference on Modelling and Simulation, Krakow, Poland, pp. 608–615 (2011)Google Scholar
  17. 17.
    Cohen, M., Kamesam, P.V., Kleindorfer, P., Lee, H., Tekerian, A.: Optimizer: Ibm’s multi-echelon inventory system for managing service logistics. Interfaces 20, 65–82 (1990)CrossRefGoogle Scholar
  18. 18.
    Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Systems 9, 115–148 (1995)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Deb, K., Goyal, M.A.: Combined genetic adaptive search (geneas) for engineering design. Computer Science and Informatics 26, 30–45 (1996)Google Scholar
  20. 20.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Transactions on Evolutionary Computation 6(2), 128–197 (2002)CrossRefGoogle Scholar
  21. 21.
    Deuermeyer, B., Schwarz, L.B.: A model for the analysis of system service level in warehouse/retailer distribution systems: The identical retailer case. In: Multi-Level Production/Inventory Control Systems: Theory and Practice, North-Holland, Amsterdam, pp. 163–193 (1981)Google Scholar
  22. 22.
    Dong, M., Chen, F.F.: Performance modeling and analysis of integrated logistic chains: An analytic framework. European Journal of Operational Research 162(1), 83–98 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Fonseca, C.M., Fleming, P.J.: An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation 3(1), 1–16 (1995)CrossRefGoogle Scholar
  24. 24.
    Fu, M.C.: Simulation optimization. In: Proc. of the 2001 Winter Simulation Conference, pp. 53–61 (2001)Google Scholar
  25. 25.
    Fu, M.C.: Optimization for simulation: Theory vs. practice. INFORMS Journal on Computing 14(3), 192–215 (2002)CrossRefGoogle Scholar
  26. 26.
    Fu, M.C., Andradóttir, S., Carson, J.S., Glover, F., Harrell, C.R., Ho, Y.C., Kelly, J.P., Robinson, S.M.: Integrating optimization and simulation: research and practice. In: Proc. of the 2000 Winter Simulation Conference, pp. 610–616 (2000)Google Scholar
  27. 27.
    Glover, F., Kelly, J.P., Laguna, M.: New advances and applications of combining simulation and optimization. In: Proc. of the 28th Conference on Winter Simulation, pp. 144–152 (1996)Google Scholar
  28. 28.
    Graves, S.C.: A multi-echelon inventory model for a repairable item with one-for-one replenishment. Management Science 31, 1247–1256 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P.H.E.: Handbooks in Operations Research and Management Science: Logistics of Production and Inventory. Elsevier, Amsterdam (1993)Google Scholar
  30. 30.
    Hopp, W.J., Spearman, M.L., Zhang, R.Q.: Easily implementable inventory control policies. Operations Research 45, 327–340 (1997)zbMATHCrossRefGoogle Scholar
  31. 31.
    Jensen, M.T.: Reducing the run-time complexity of multiobjective eas: The nsga-ii and other algorithms. IEEE Transactions on Evolutionary Computation 7(5), 503–515 (2003)CrossRefGoogle Scholar
  32. 32.
    Kang, J.H., Kim, Y.D.: Coordination of inventory and transportation managements in a two-level supply chain. International Journal of Production Economics 123(1), 137–145 (2010)CrossRefGoogle Scholar
  33. 33.
    Kiesmüller, G.P., de Kok, A.G.: A multi-item multi-echelon inventory system with quantity-based order consolidation. Working Paper, Eindhoven Technical University (2005)Google Scholar
  34. 34.
    Klingebiel, K.: Entwurf eines Referenzmodells für Built-to-order-Konzepte in Logistiknetzwerken der Automobilindustrie. Unternehmenslogistik. Praxiswissen, Dortmund (2009)Google Scholar
  35. 35.
    Klingebiel, K., Li, C.: Optimized multi-echelon inventory policies in robust distribution network. In: Proc. of 25th European Conference on Modelling and Simulation, Krakow, Poland, pp. 573–579 (2011)Google Scholar
  36. 36.
    Konak, A., Coit, D.W., Smith, A.E.: Multi-objective optimization using genetic algorithms: A tutorial. Reliability Engineering & System Safety 91(9), 992–1007 (2006)CrossRefGoogle Scholar
  37. 37.
    Kuhn, A., Klingebiel, K., Schmidt, A., Luft, N.: Modellgestütztes planen und kollaboratives experimentieren für robuste distributionssysteme. In: Tagungsband des 24. HAB-Forschungsseminars der Hochschulgruppe für Arbeits- und Betriebsorganisation, Stuttgart (2011)Google Scholar
  38. 38.
    Miranda, P.A., Garrido, R.A.: Inventory service-level optimization within distribution network design problem. International Journal of Production Economics 122(1), 276–285 (2009)CrossRefGoogle Scholar
  39. 39.
    Ólafsson, S.: Metaheuristics. In: Handbooks in OR & MS, vol. 13, pp. 535–574. Elsevier (2006)Google Scholar
  40. 40.
    Pasandideh, S.H.R., Niaki, S.T.A., Tokhmehchi, N.: A parameter-tuned genetic algorithm to optimize two-echelon continuous review inventory systems. Expert Systems with Applications 38(9), 11, 708–711, 714 (2011)Google Scholar
  41. 41.
    Sherbrooke, C.C.: Metric: a multi-echelon technique for recoverable item control. Operations Research 16, 122–141 (1968)CrossRefGoogle Scholar
  42. 42.
    Simchi-Levi, D., Zhao, Y.: Safety stock positioning in supply chains with stochastic lead times. Manufacturing & Service Operations Management 7, 295–318 (2005)CrossRefGoogle Scholar
  43. 43.
    Svoronos, A., Zipkin, P.: Estimating the performance of multi-level inventory systems. Operations Research 36(1), 57–72 (1988)zbMATHCrossRefGoogle Scholar
  44. 44.
    Tekin, E., Sabuncuoglu, I.: Simulation optimization: A comprehensive review on theory and applications. IIE Transactions 36(11), 1067–1081 (2004)CrossRefGoogle Scholar
  45. 45.
    Tempelmeier, H.: nventory management in supply networks. Problems, models, solutions. Books on Demand, Norderstedt (2006)Google Scholar
  46. 46.
    Terzi, S., Cavalieri, S.: Simulation in the supply chain context: a survey. Computers in Industry 1, 3–16 (2004)CrossRefGoogle Scholar
  47. 47.
    Wagenitz, A.: Modellierungsmethode zur Auftragsabwicklung in der Automobilindustrie. Unternehmenslogistik. Verl. Praxiswissen, Dortmund (2007)Google Scholar
  48. 48.
    Yu, X., Gen, M.: Introduction to evolutionary algorithms. Decision Engineering. Springer, London (2010)CrossRefGoogle Scholar
  49. 49.
    Zipkin, P.H.: Foundations of Inventory Management. McGraw-Hill, New York (2000)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Chair of Factory OrganisationTechnical University of DortmundDortmundGermany
  2. 2.Department of Supply Chain EngineeringFraunhofer Institute for Material Flow and LogisticsDortmundGermany

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